this is relatively easy to do, if you know how to read a Mulitmeter and know how to solder. I own 2 Stilettos, but I'm not near either of them, atm, so I'm doing this from memory.
the original footswitch/cable is a TRS(tip-ring-sleeve) type, or Stereo. tip will be one 'channel' or function, ring another and sleeve would be the ground. this cable plugs into original Stiletto footswitch and is then split between the 2 footswitches for Solo and Channel selection. If you open up your existing switch, you'll see how this works, and I recommend doing that, just so you know for the future.
What you want is to find, from the original switch/cable, the one that switches the channel and NOT the solo boost.
Let's Pretend it's the Tip of the stereo cable you want to switch the channel - remember, I'm NOT saying it is, you need to use an Ohmmeter to figure that out, on the multimeter. do this without plugging the cable into the amp.
So, from the original stereo cable, imagine using one end to plug into your amp, (*as you've done before), and having the other end of that cable to a Tip Sleeve plug, (*or a Regular Mono guitar cable) - Make Sense?
IF you have a single button footswitch and a guitar cable you don't mind rewiring, all you would need to buy is a Stereo(TRS) plug and you can make this work.
With the Stereo Plug and wire the connection needed, (*The Tip of the stereo plug), then wire the ground, or sleeve to the other connection, leaving the Ring connection Un-soldered to anything.
Now, using this cable you've made, plug the stereo end into your amp, and the mono end into any single button On/Off switch, and TA-DAaaa, you're done.
Hope that helps.