First, stay calm and clean as much of the paint off your smeargle as possible. He may not like a bath, but you’ll need to make sure he doesn’t accidentally lick any of it off. You can encourage him to produce new pigments from his tail with a healthy diet later.
As you’re cleaning him, check around the mouth again, just to be sure he hasn’t eaten any. If you don’t see anything, you’re likely fine; unlike many other dog pokémon, smeargle are more interested in using paint than eating it outright.
Still, keep an eye on him for the next few hours. If he begins vomiting or displaying any other sign of digestive upset, take him to the pokémon center immediately or call your region’s pokémon poison control hotline—preferably the former, as a trained Nurse Joy will be able to handle his recovery from there.
Best of luck!