Lexicographer and phonologist John Walker (1732–1807) published a pronunciation dictionary in 1798 called A Key to The Classical Pronunciation of Greek, Latin and Scripture Proper Names, or for short, simply "Walker's Key". In much the same way that "Webster's Dictionary" became a term for anything notionally derivative of Noah Webster's early work, "Walker's Key" became a term that others used for derivative later work, for much of the century that he only lived to see the first few years of. For all of the 19th century, Walker's Key not merely stayed in print, but in fact went through dozens of printings and editions.

For several decades, the system for Walker's Key was that each word had syllable boundaries and stress marks; for any given word, you would take that, and apply a system of several phonological rules, and then you would have the correct pronunciation. The number of rules varies from phrasing to phrasing and author to author— as many as 31, as few as 9.

(In a manner not unknown in modern linguistics, each word's syllable-boundaries are chosen, unpredictably, to trigger the application of different rules that depend on context of stress and syllable boundaries. For example, the first two syllables in Abii and Abila are syllabified differently: A'bi-i but Ab'i-la.)

In my opinion, Walker's Key is best understood not through an earlier edition, but through three revisions, decades after Walker's original work:

⁂ Webster/Goodrich adds more entries, and also has a grouping of names by their ending and stress pattern:

Google Books # gmwIAAAAQAAJ
· Author: Chauncey A. Goodrich, Noah Webster
· Title: A Dictionary of the English Language; [...] to which are added [...] Walker's Key [...] revised and enlarged by Chauncey A. Goodrich [...] Tenth Edition, Revised and Corrected, 1866
· Publisher: George Routledge & Sons, London 1866
· PDF file: 185,315,040; 1297π pages
· The volume is mostly a general dictionary. The Classical section is pages p1184π - p1246π. For the syllabified names, p1184π - p1231π. For names grouped by combination of word ending and stress pattern, p1232π - p1267π.

⁂ B.H. Smart changes Walker's system a great deal, and the thirty-odd rules are replaced by nine observations/explanations/directions. He shows stress better: unstressed syllables are italicized; and in longer words, he notes primary vs secondary stress as necessary. There are many additional entries. But whereas the main body of the dictionary is completely rewritten from Walker's dictionary, the Walker's Key appendix isn't greatly "remodelled", just made clearer.

Google Books # 76ERAAAAIAAJ
· Author: Benjamin Humphrey Smart, John Walker
· Title: "Walker Remodelled: Smart's Pronouncing Dictionary of the English Language, [...] With a Key to the Pronunciation of Greek, Latin, and Scripture Names" , 1871.
· Publisher: Longman, Green, and Co., [et alii], London, 1871.
· PDF file: 51,126,460 bytes; 743 pages by PDF pagination.
· The Classical section is pages 697π-734π; by the printed volume's pagination, it's p654-p690.
· At points where the scan is hard to read, you might want to consult a generally better scan of a much earlier edition, GB# vDJiAAAAcAAJ: Walker Remodelled. A New Critical Pronouncing Dictionary[...], 1836, although its nine rules/observations that cover the data are, in theory, different.

⁂ J.E. Worcester's work is based on Walker's, but has a completely different notation, to be the same as the notation in the rest of the dictionary; and this allows him to simplify Walker's system, to barely 13 rules.
He states (p488π) his relation to Walker's Key: «The Initial Vocabulary of that work [Walker's Key in 1798] contained about 10,500 names; and an edition of that work, by W. Trollope, with about 550 names, was published in 1833. Of the names found in Walker's "Key," about 2,200 have, in the following Vocabulary, been rejected as useless in a pronouncing vocabulary; and Walker's pronunciation of about 500, having been shown by citations from the Latin poets given in the works of Carr and Sharpe, and by other prosodists, to be erroneous, has been corrected; and besides these, there are about 150 names of which Walker's pronunciation is doubtful. All the names in Walker's Vocabulary, with respect to the pronunciation of which there can be any difficulty or doubt, are here given, and in addition to them, about 6,580 names which have been herived from the works of T. S. Carr and L. Sharpe, Pauly's Real-Encyclopädie, the Classical Dictionaries edited by Dr. William Smith, and various other sources.»

Google Books # QPYvAAAAYAAJ
· Author: Joseph E. Worcester
· Title: A Dictionary of the English Language, by Joseph E. Worcester, LL. D. / Revised, and with Important Editions, 1866 [may actually be 1860]
· Publisher: Swan, Brewster, and Tileston, Boston, 1866 [may actually be 1860]
· PDF file: 50,861,504 bytes; 623 pages by PDF pagination

⁂ Anthon and Smith's Dictionary is an encyclopedic dictionary of classical names. There is no separate pronunciation section— instead, the headword in most entries marks the vowel length for the English pronunciation of the Classical names, which is generally enough to give the correct pronunciation— least to exclude most potential but incorrect forms. I suggest consulting it when Walker's Key is unclear or unhelpful.

Google Books # 9-4rAAAAYAAJ
· Author: Charles Anthon and William Smith
· Title: A New Classical Dictionary of Greek and Roman Biography, Mythology and Geography, Partly Based Upon the Dictionary of Greek and Roman Biography and Mythology by William Smith, LL.D., Editor of the Dictionaries of Greek and Roman Antiquities, and of Greek and Roman Biography and Mythology, 1895
· Publisher: Harper & Brothers, New York, 1895
· PDF file: 99,713,412 bytes; 1069 pages by PDF pagination
· It makes a note of providing the Greek original. So the entry "Aphidas", has the headword Aphīdas and follows it with: Ἀφείδας

⁂ The basic notation (dashes and stress-marks) is similar, but its rule system has no relationship to Walker's Key as far as I can tell. It has a number of names not found in the above resources, in one or other of its two Classics-relevant appendices. I suggest consulting Annandale when Walker's Key and Anthon & Smith are unclear or unhelpful.

Scans of the pertinent excerpts are online.
· Author: Charles Annandale
· Title: The Concise English Dictionary, Literary Scientific and Technical, with Pronouncing Lists of Proper Names and of Foreign Words and Phrases— Key to Names in Mythology and Fiction— And Other Valuable Appendices [...] , ~1925.
· Publisher: Blackie & Son, ~1925
· As a single ZIP file: ~90MB.

Ideally, everything in these incidental works is included in the above Older Works, or is superseded by them, but I'll list these for completeness.

• Smart 1836 — Walker's Key in GB# vDJiAAAAcAAJ: Walker Remodelled...— A New Critical Pronouncing Dictionary of the English Language [...] and Accompanied by [...] a Key to the Pronunciation of Greek, Latin, and Scripture Proper Names.
• Walker 1798 — Walker's Key in GB# _-1DAQAAMAAJ : A Key to the Classical Pronunciation...— of Greek and Latin Proper Names [...]: To which is added, a Complete Vocabulary of Scripture Proper Names [...] Concluding with Observations on the Greek and Latin Accent and Quantity
• Walker 1822 — Walker's Key in GB# _LVfAAAAcAAJ : A Key to the Classical Pronunciation...— of Greek, Latin, and Scripture Proper Names; [...] Concluding with Observations on the Greek and Latin Accent and Quantity; [...] The Seventh Edition
• Walker 1830 — Walker's Key in GB# BWoUAAAAYAAJ — A Key to the Classical Pronunciation...— of Greek, Latin, and Scripture Proper Names; [...] Concluding with Observations on the Greek and Latin Accent and Quantity; [...] The Ninth Edition
• Smith 1878 - GB# fZUOAAAAYAAJ — A Smaller Classical Dictionary of Biography, Mythology, and Geography
• Smith 1853 - GB# QlQJAAAAQAAJ — Dictionary of Greek and Roman Antiquities
• Anthon and Smith 1843 - GB# 9e8rAAAAYAAJ — A Dictionary of Greek and Roman Antiquities
• Smith 1873: A Dictionary of Greek and Roman Biography and Mythology. By Various Writers. Edited by William Smith [...] in Three Volumes

  v1 (Abaeus—Dysponteus) = GB# 4pcPAAAAYAAJ
  v2 (Earnius—Nyx) = GB# VzMGAAAAQAAJ
  v3 (Oarses—Zygia) = GB# R6c_AAAAYAAJ

• Smith 1872: Dictionary of Greek and Roman Geography. Edited by William Smith [...] in Two Volumes

  GB# _sYPAAAAYAAJ - v1 (Abacaenum - Hytanis)
  GB# L55QAAAAYAAJ - v2 (Iabadius - Zymethus)