Timed one-shot circuit to drive laser module
Several options:


A solenoid driver circuit is probably pretty robust. You need to worry about the strong currents driving the solenoid, and the flyback voltage generated when the solenoid is discharged, affecting your laser driver circuit much more than you need to worry about a laser driver circuit disturbing the solenoid driver. So a simple option is just connect a buffer to the solenoid driver signal, make sure any overvoltages can't get through it, and use that to drive the laser.
Use an off-the-shelf monostable multivibrator like 74LV1G123 (for example). The datasheet will clearly explain how to trigger it and how to control the output pulse duration.
As mentioned in comments, use a tiny microcontroller. This is a good solution if you want the output pulse to last more than 0.5 s or so. If you want a shorter output pulse, I expect the multivibrator solution will have less total complexity.