E-grip would be the easiest. Put a button anywhere (as noted above). Otherwise using a ram and making it pneumatically activated would also work, but would require a regulator for the pneumatics. So, an E-grip would be the simplest.
For the rest of it:
I would build some sort of angled ramp above the marker to be filled with paint and then use a 13ci tank/CO2 tank for the air source with a remote, since it would fit in the briefcase then. I don't think it would be terribly hard to do.