I'd use a Q-tip, with isopropyl alcohol or some such.

Best practice is probably to turn off the device, remove the battery, clean it, and shake it dry, then let it sit for a while (with the headphone jack down) to evaporate/drain any remaining solvent before reinstalling the battery.

Thoughtfix's disassembly video is, of course, a good first stop if cleaning doesn't fix it, and you want to try effecting a repair yourself.