What do you want the momentary switch to do ?
If you want it to do the whole 3PDT switching, I doubt very much that you will find a momentary switch of that complexity - I’ve certainly never come across one.
You could, however, use a single pole momentary switch to pull in a 4-pole change-over relay (non-latching, of course).
How you would interface the relay and the existing 3PDT footswitch, however, is a different matter - which we can’t help you with until you answer the question above.
”Sex is great - but you can’t beat the real thing !” - The Wanker’s Handbook