Thanks Tonydragon!
I've painted only two Nerf guns over the years, and for the first one, I did take it apart, but mainly because I had modified parts of it. For this particular piece, I painted it as is. The spray paint really doesn't really affect the moving parts at all, at least in this particular case, as the paint tends to go on thin and quite flat. The only real exposed moving part on this blaster is the bottom "pump" portion for the darts. I did end up using a brush and some enamel paint to touch that area up, as there are hard to reach spots. The paint around that area doesn't seem to rub after it dried because there appears to be enough space between the moving parts, which worked out.
I did plug up the holes on the barrel with some bits of paper towel, where the lights are, to prevent any paint from getting in there.
But basically, if you spray layers of thin coats of paint, the paint never really gets wet enough or plentiful enough to actually interfere with the moving parts.