I vote for Al Cohn as the tenor player. (Too bad they only show his hands during the solo).
As I recall, Scott was married to the featured singer Dorothy Collins at the time. Took home two healthy paychecks from that show...
Too jowly for Al at that time, I think, also looks about 10 or more years too old for him, and it sure doesn't sound like Al -- a kind of proto-Sam the Man Taylor vibe. Maybe Al Klink, who could sound like anyone on cue.
Boy, I used to think Dorothy Collins was cute, which is kind of pathetic in retrospect -- going for that scrubbed, nice-girl image and the rabbity slight-overbite. An extension of the teacher's crush, but what are you going to do at age 12 or so? IIRC, the Collins-Scott marriage ending in severe strife.
You're right - Al never sounded remotely like this player. Is the soloist actually the taller non-spectacled guy? If it is he looks and sounds a bit like Mickey Folus, who was unlucky enough to sit next to Flip throughout the first herd, and a very good soloist in his own right. The arrangement sounds like Buster Harding.