Shimano front derailleur specs list the maximum changing size, i.e., teeth. I'm waiting on a FC-T4060 crankset (44/32/22) that I'd like to use with a M4000 Altus front derailleur. But specs for the derailleur say max chainring size 40t.

Can I cheat it or would that be asking for trouble?

If it is a standard clamp on, don't sweat it. It will be fine.

What is the smallest chainring that Campagnolo produced in the 1980s

almost certainly a 39. I imagine they were using 135mm BCD cranks, which limited things to 39. Not sure if they had road triples in the 80s, and the track crank sets were 144mm BCD IIRC

Apparently Campag brought out Euclid in late '88 to go on '89 model year mountain bikes. They appear to have offered a 24 chainring;
MOMBAT: Campagnolo mountain bike component History

You can probably cheat, but you may want to set the derailleur height close to where it would be if it were a 44t.

I have found when going to a smaller than recommended outer chainring, that setting it with a larger chainring/cage gap helps the upshift from middle (triple) chainring. I haven’t had an issue downshifting with the larger gap. But you do need to experiment to find the best setup.

John

Depends on what crank. Record and Super Record 144mm BCD road doubles minimum tooth count was 41. Record triple was 36, although 3rd parties made compatible rings down to 30T. Triomphe and Victory 116mm BCD was 35T.

The curve of the derailleur won't exactly match the circumference of the chainring, but it'll be close enough to work. I've learned that you can mis-match them by quite a lot. The biggest concern is that you'll go past the total teeth difference that the derailleur can handle. For a triple, that's usually 22-24 teeth. I'm currently running a 58T ring on my trike, with a derailleur that's designed for 53T.