The way I would do this myself, to be both satisfying and physically quite accurate is to use “sticky particles”, like real paint. You could make the paint nozzle a particle emitter, and actually “spray” particles of paint down on to the geometry. Then program the particles to freeze in place on collision with the object, just like real paint. This way you could run the particle emitter over any geometry and the paint would travel out in a straight line until it intersects with the geometry and then it stops. It would effectively coat the object in particles and give the illusion of a real paint effect. You could vary the density, size, color of the particles to make any color paint, thickness and coverage.
As to how to actually do this, I would have to ask for help from our physics expert, but I am sure is it easy to use particles and additional code to get them to freeze on collision.