I don't know if it's possible to call an Exe directly, but you can call a function in an external DLL. Your DLL would then launch the EXE.
I would suggest though that you really should try to move the Exe code onto the database if possible. Is this your own executable (ie can you modify it?). If so, you might consider signalling your already running executable to perform some work via DBMS_ALERT.SIGNAL.
Trigger->Dll->Exe - I have no idea what would be occurring in terms of transactions (what's commited etc). I think it could get messy :-(