A:Answer I'm generally aware of countertop push buttons but have never had that kind. But electrically, I'm assuming the wiring from your push button goes into an electrical box of some sort on the backwall under your sink. I'm also assuming that power comes into that same box as well (normal black + white + green/ground). So with these 2 assumptions, you should be able to wire-in the new disposal with the appropriate 2-wire plus ground cable (coming from the disposal). If you had an older disposal that you're replacing, then duplicating the electrical connections in that box should be straightforward.
The Evolution Excel installation instructions basically show what I've described. It simply presumes a switch of some sort -- whether on the wall above the sink (as shown per their diagram), -- or otherwise. I'm just not familiar with the type of protections needed by a countertop switch (basically preventing moisture from getting to the wires).
Hope this helps.