I have the tubing attached to the top of the trigger, so I can operate it one-handed, point-and-shoot style. I would like to keep that form factor and I'd rather not try to modify the trigger with the push-button. Had I known this is the way I was going to end up going, I would have looked for a latching or even a toggle trigger instead of the momentary switch. Hindsight, etc., etc.
I think a relay will be the best option. I'll add a 3-way switch after the 87 and 87a contacts and use it as the main switch. One way will be powered off unless triggered, and the other way will be powered on unless triggered.