The Sox had a really good pitching staff. In addition to Wilhelm and Fisher, they had Tommy John when he could throw hard, Gary Peters, Joel Horlen, Juan Pizarro, and several other established pitchers who were at the ends of their careers.
Unfortunately those mid-60s teams didn't hit very well; and if I am remembering correctly, they used several catchers - Sherm Lollar (not sure when he retired), John Romano, JC Martin (of '69 Mets shoe polish fame), Cam Carreon, and a cast of lesser names as if the names on my list aren't lesser enough.
I'd guess Romano; and if not Romano, Martin. I know it wasn't Smokey Burgess. He didn't log much time behind the plate at that point in his career.
I can't remember what I had for lunch yesterday, but take me back to ages 10 - 12 and I'll give you both Chicago teams' lineups and several others too.