Not sure I can add much to your quest, though our's intersects in some ways. My ancestor, Captain Thomas Hollingsworth (whom my impression is based upon), is to have had some sort of dealings with Wake that I'm trying to sort out (apparently he originally was meeting Wake with supplies). According to some documents provided to me by a Hollingsworth cousin:
In the Calendar of (British) State Papers, Colonial, America & West Indies, Volume containing correspondence, etc., for the years 1696 & 1697, (Huntington Library, San Marino, Calif.) : (p.259 et seq.):
"East India House #517. Secretary to the East India Company to William Popple. Forwarding certain documents respecting certain ports in America from which the ships concerned in the late piracies in the Red Sea where set forth, (signed) Ro. Blackborne (Endorsed) Dec. 18, 1696. Annexed: (517 i) T. South to the Lords Justices of Ireland. Dublin, 15 August, 1696.
"The best place to send shipping to meet the pirates is to Fernando, an island in latitude 3 or 4 degrees where they must touch to water in Feb., or March. The owners of Capt. Wake's ship live in Boston, New England, and were going in a brigantine to bring clothes and necessities to meet him at Fernando; but hearing that we were coming to Providence they followed us thither but did not arrive till after we came away. THOMAS HOLLINGSWORTH now sailed from Galway will meet Wake at Providence, where Wake will certainly be within six or eight weeks, or else not till after Christmas. HOLLINGSWORTH left money for Governor Trott. Wake had already had a pardon for piracy in King James's time... All the ships that are now out (except Tew, from New York & Want, from Carolina), are from New England. They build their ships in New England..."
(Ibid, Volume for 1700. Page 277, citation #466 xi) "Examination (dated March 25, 1700) of James Brown who sailed from Rhode Island in 1695 on the Susanna, Thomas Wake, Commander, as a privateer with a Commission from the Governor or Deputy Governor.
"The company were all upon shares. In the seas of India they met with the Phancy, Henry Every, Commanding, who plundered the Susanna. Examinant being weary of being aboard in those parts, with one Capt. Smithsend, and THOMAS HOLLINGWORTH (sic), embarked on the Phancy, which was then designed for Providence."
(NOTE: Captain Kidd is referred to in the same group of papers.)
Amongst the notes sent to me was a listing of the Red Sea pirate fleet (I'm not sure of the source, if it's part of the UK Nat'l Archives or what?):
Henry Avery (aka John Avery, Long Ben/Capt. Bridgeman) (1665-1728?). In September 1695, Avery's ship, Fancy waited outside Mocha for the pilgrim fleet to arrive. Avery was joined by several American pirates:
Captain Joseph Faro on Portsmith Adventure from Rhode Island
Captain Want on Dolphin from Philadelphia
Captain William Maze on Pearl from Rhode Island
Captain Thomas Tew on Amity from New York
Captain Wake on Susannah from Boston
What little of the rest of the documentation I have is about my ancestor Thomas Hollingsworth, and his association with Henry Every (Hollingsworth was amongst those sent to attempt to negotiate a pardon for Every with Govenor Trott, and he later captained the ship"Issac" that returned some of Every's crew to Dublin, Ireland -- Hollingsworth himself later being chased up the Dublin River by a French privateer).
(517 iii-ibid) "Narrative of Philip Middleton, of the Ship Charles Henry, to the Lords Justices of Ireland, given on 4 August, 1696 :
"... another sloop commanded by HOLLINGSWORTH was chased into Dublin by a French Privateer. She had 16 more of the crew of Charles Henry aboard."
I hope this helps in some small way. I find it interesting that according to the examination of Brown, Every looted Wake's ship, the Susannah, and Hollingsworth, Capt. Smithsend & James Brown came aboard the Fancy.
Anyhow, as mentioned earlier, I too seek any info regarding Wake, to help flesh out my own impression
Your ol' shipmate ~
Capt'n Hollingsworth