Sounds worthwhile to try. You could put a seperate momentary switch below the right trigger so that when you push the trigger it pushes the button. That's how the push reactive lights were originally done.
Also, when you're messing with the flash circuit,be careful. It works by charging a very large capacitor, and then discharging it all at once to create the flash. If you accidentally discharge that on your finger or somthing, it's gonna hurt, bad. It may also damage the psp circuitry if the cap is discharged into it by mistake.