Like your avatar. I was in 1/75th, the 5th SFG and the 3rd SFG.
Starter switches are almost always wired somewhere with a relay. The relay reduces the high amount of amps that goes thru the starter circuit when the starter is engaged
Imagine this: Ever have a motorcycle? Ok, the small little starter switch mounted on the handlebars has super small gauge wires leading to it. If it didn't have a starter relay to reduce the amount of amps going thru it when the starter was engaged, it would heat up, smoke and melt in about one second.
On your Cuda its the same deal: You have that small little black box (your relay) mounted near the battery on the drivers inner fender well. It serves the same purpose. It keeps your small gauge wires at your ign switch (and harness) from frying when the starter is engaged
The starter draws the highest amp load on its associated wire harness when engaged, hence the relay
To answer your question, any switch you use, without a relay somewhere, is going to get hot, really quick. Here is an example. Lets say I wanted to start my car by just jumping with a very large gauge cable directly to the starter. That cable will get very hot, very very quick.
So to answer: I really don't know how many amps (with a relay) would go thru any starter switch, but Ill guess its not more than say 20-30 amps, solely because I haven't seen any fuses or fusable links rated at more than 30 amps
So running any switch, or button, without some sort of relay, would be a non-starter in my book (Pun intended). Not saying thats your plan, but some folks don't know the purpose of a relay
Good luck