I've modded a Rapidstrike and im working on a Hyperfire, so of the 2 i'd go the Hyperfire for the amount of stuff you want to cram into it. It has a good amount of empty space in the orange section at the front, and if you cut out the insides of the battery box, you'll get a huge chunk of room in the rear too.
Theres not a lot of empty space in a Rapidstrike at all.
What you're proposing will work to drive the motor, but, the time to run the motor will vary by voltage. If you run it from a lipo it will turn faster so need to run less time.
Instead, use a switch to detect when the firing plunger has fired, and then stop the motor. Don't need to time anything then, can just run the motor until the switch is pressed.
I'd also put a pull down resistor on the arduino pin driving the transistor. Otherwise when the arduino turns on, the voltage on that pin might briefly go high and run the motor. Also, think about using a h-bridge instead of transistor. Can run it from a pwm arduino pin and control the speed more accurately.