I'm not sure that's possible in the sense that you're talking about.
You can eliminate the toolbar by making the vi appear as "dialog"
(Right Click on VI icon [top right front panel]->VI
properties->window appearance->dialog), or you could customize it.
But to run the
vi itself cannot be done by a button click, as
the vi has to be running in order to register that click. What
you could do, is run the vi on start, then have it hang on maybe an
event structure or default case of a state machine until the "start"
button is clicked.