Sure you can!
All you have to do is have the button run a macro which
uses the "RunApp" action. From there, all you need to put
in the command line are the program's filepath and the
document's filepath. Both are accessible if you use
the "Run" command from the start menu (just browse and you
can find your file). Copy the program's path and then the
document's path into the command line and it should work.