Here's Wes in the studio in front of an Ampeg Gemini I. Of course, Ampeg's were in every NYC studio in the 60's. Wes played Fender Supers, and Twins. He was discerning about amps, and played the speaker game (maybe he went back and forth between Jensens, JBLs, alnicos and ceramics??). In a Guitar Player interview he talked about the speakers being the most important part of the gear setup because it is what you ultimately hear, and he indicated he was never happy with his sound. He also played Standels. Grant Green played twins (tweed?) and ampegs, Jim Hall used a GA50, Tal Farlow played gibsons and twins.

Then when SS hit, guys like Joe Pass and George Benson switched to Polytones and Roland JC's. The SS stuff is a lot lighter than tube stuff, and companies like Polytone and Roland seemed to be happy to cater to jazz dudes in the 70s, while, clearly, ampeg and fender were focusing elsewhere.
so, for your question "Would any of the usual vintage Fenders be a good choice ?"
I'd say, for a fender, an SS recto, fixed bias push-pull model, that is loud enough with the guitar player's pickup for whatever size room or volume he wants to play at.... bandmaster...? super? twin?
clean is key for jazz tone.
almost any amp will distort at max volume, so I think these guys liked an amp if they could play loud enough without distorting at whatever room they played. original jazz guys played P90 and 59 style humbuckers instead of telecasters. I suspect most jazz dudes thinking about tone are looking to Green/Burrell/Montgomery/Pass/etc who all played all lower impedance p/u'd compared to modern PUs, and tele's. I don't know when the strat came into the jazz guitar picture, (maybe with Robben Ford? ) Roy Buchanan plugs into a JC and its sweet SS compressed OD city. jazz guys also didn't like carrying heavy amps (i don't think there was enough money in jazz guitar to afford amp toting roadies, not unless Benson probably), that why ampeg had the ampeg-turn-key guitarist club, or whatever they called it., and its why polytone minibrutes were popular.
a great jazz tone was Les Paul. what did he play? low-impedance pickups into transformer preamps into Gibsons or direct into the board?