It depends on if you want to be OSHA and EPA compliant, or if you just want to shoot the crap outside so it doesn't bother YOU... I would think that a simple piece of PVC junction would combine the two vents into one, which can then be directed outside the house via a flexible dryer vent.
I'm not sure what the stages of filtration are, but being a Rube Goldberg disciple, you could probably figure out some sort of rig with Heppa vacuum filter or an auto air filter at the exhaust of the system to catch particulates and keep a paint haze from forming on your siding.
Lee