I have a modern campagnolo record headset on my bike right now. Would I be able to switch to a c-record headset or would the steer tube be cut too short for that?

I think the steertube may be to short, the crecords are kinda tall. I did some quick googling and couldnt turn up stack hight info on the c rec (c is short for corsa) but came up empty. Campagnolo Record (current) is 36.5 mm.

I've dug into some old catalogs and can't find the stack height either. You're probably going to have to try and see.

I once switched out an old FSA threaded headset which looked to have a "standard" stack height for a C-Rec and there was plenty steerer tube available. I don't think they are that much taller, despite their appearance. Only one way to find out, unfortunately.

The best I could come up with is from the 1998 catalog. The Veloce headset, which appears to be a similar design to the C-Rec headset, is listed to have a stack height of 40.5mm.

waitasec - c-record was a gruppo from late 80' meaning there are only threaded headsets for it, AFAIK. I presume you have a modern threadless one. I can measure the tack height of a threaded c-record headset on my bike tomorrow, if you can not find the stack height earlier.

I still have the box of '94 record headset, according to the paper the stackheight is 40.5 mm. If the current one has a stackheight if 36.5 mm, it won't fit.

Campy still makes a threaded Record headset.

You could say that if you knew how much steerer tube he has to work with. But since we don't, you can't.