How to VERIFY that a "Run Once" application has run

I am trying to force run an install to all of my users. The install file
is an exe. I want to see which users have already run the application.
Is there a way to do this since we have far to many machines to visit
each one? Is there a way to use NLIST to do this? I know I could do an
NLIST on last login time, but that doesnt necessarily verify that the
application object has run.
Thanks.