I was just about to start writing something like this myself, when I saw this comment. Unfortunately, I realized it wasn't that easy just after. There are two major reasons.

The first is that windows will often allow you to run programs that aren't on your path, if they're registered properly in the Registry. Specifically, if HKEY_(LOCAL_MACHINE|CURRENT_USER)\Software\Microsoft\Windows\CurrentVersion\App Paths\$exe exists, and has it's default value set to an existing file... I think. There seem to be some cases on my machine that would indicate a more complex pattern.

The second is that there are other executable extensions, beyond the common .exe. There's .com and .pif, .bat, and on NT, .cmd. In fact, CMD (the shell under NT) allows you to set whatever you want to be considered as executables; echo %PATHEXT% at a prompt (or perl -e 'print $ENV{PATHEXT}', if you prefer).

Update: Fixed spelling errors.