Noice from fan in Audio Research VT 100 MK III

It's is very easy to replace the fan. If you can use a Philips screwdriver you can do this. There is no soldering required. Place the amp on its side and the rest is easy. Just make sure the amp has been off an unplugged for a few hours. The wire that goes to the fan is a little 2 conductor plug. Four screws hold the fan in place.

Fans are easy to remove and clean or replace. I've done it with ARC amps and with my composting toilet fan several times.

Did you try to vacuum it or clean it with a Q-tip for dust binding up the blades?

Try cleaning it, fans will increase noise as blades pickup dust dirt hair etc.