Doesn’t sound like anything a careful application of RTV can’t handle. It can be found in small squeeze tubes at most auto parts stores, where it might be sold as ‘liquid gasket’ or something similar. You can also get it at hardware stores in large tubes meant to be used in caulking guns.
If the original gasket still looks good, no cracks or breaks in it after you remove the cover, I’d wager it will still be water proof after you put it back on. If it’s damaged, I would try to remove it entirely, and likewise, if the replacement cover doesn’t have a seal, you would want to apply some RTV or similar sealant. Ideally, I would use a syringe for this. In the US at least, you can buy needles at a pharmacy without a prescription, you just have to ask for them at the pharmacy counter. Suck some RTV into the syringe, and apply it carefully on the sealing surfaces of the cover. Put the cover on before the RTV dries so it mates to the surfaces, give it about an hour to cure, and it should be water proof.