Do you already have a filter in the tank? If so, then you don't need an air pump, though you may want to make sure the intake on your filter isn't strong enough to suck a shrimp in. Putting a pre-filter sponge, or wrapping some filter floss around the intake, is all you need to do.
If you don't already have a filter in the tank you want to keep shrimp in, you'll want to add one- shrimp are very sensitive to water conditions, and having a filter so you can cycle the tank is enormously helpful in keeping shrimp (and any other critter) healthy. That said some people are successful at keeping shrimp in filterless tanks if they have a large number of plants, but I've never tried it so I can't give any specific advice there.