any vintage bike that originally came with tubular wheels (AKA sew-ups, tubbies, sprints) will take 700C clincher wheels. That includes many, many bikes from the '60s and '70s, most with 5spd FWs, so the challenge then won't be brake reach but whether to re-space the rear triangle or to re-dish and short-axle a rear hub.
BTW, the first time I ever saw narrow, box-section high-performance 700C rims was in the early '80s, and they were Mavic Module E and/or Rigida 19 or 20...not rims we look for these days as they didn't tend to hold up.