Swim nappy - I actually just use the terry training pants from kmart (they have a foam insert & are just terry undies). DS has been using these since about 7-8months - but they probably would be too big at 4 months.

Shopping nappy - I agree with marcellus that a Bumgenius-style pocket nappy is a good option. I prefer these to a fitted with a cover, because it's all in one & just rolls up like a disposible would. However, I would get a Greenkids Pocket rather than a Bumgenius pocket. They are more absorbant (bamboo insert rather than microfibre) & they are made in Australia - Bumgenius is American. I've had my Greenkids since DS was born - we use them full-time (with some fitted nappies as back-ups) & they are still in great condition. They are OSFA.