DPDT's and 3PDT's are very easy to find. If you want to add an led (I'm assuming it doesn't already have one, since you mentioned it), a 3PDT would be easiest. You could also do a DPDT with millennium bypass, but that adds several extra components on a daughterboard.
Where are you located? We can probably find a source of 3PDT's or DPDT's that works for you.
If you absolutely insist on using the other switch, it can be done (assuming it is in fact a 4PST: have you done a continuity test yet?), but if you want an led, you will have to go with millennium bypass.
I've been assuming that the pedal is currently wired for true bypass. Is it?
A photo of the inside of the pedal and another one of the new switch (lug side) would be helpful too, just to be sure my assumptions are correct.