At least one of the Third Party Grading services offers a cleaning service, which they call "Conserving" and they will advise you as to whether they will clean the coin and whether it will improve it. I would think this to be a good idea unless you are very confident about your own skills.
What I would suggest is that you post pictures of the coin before doing anything. I say that because only some coins are even candidates for cleaning/conservation.
Very deep and argued constantly. All can agree that any degree of touching with any solid, be it fingers, towels or cotton swabs, has the potential to leave traces of scratching that will consign the coin to a details slab by TPG's. Rinsing with pure solvents (water, xylene, acetone) will do no harm.
You don't "clean" coins with latex gloves, they are used to keep skin oils off the coin. Wash your hands and handle the coins by the edges and you will have better control of what you are doing.
Didn't mean to be "smarty", the use of gloves to handle coins has also been extensively debated. At a coin show, how many dealers do you see using gloves? I am a chemist and have had many students want to use gloves in labs, and I discourage it since it masks your sense of feel and makes you more clumsy.
I feel cotton gloves are worse about this problem you describe. Just too much between your fingers and the coins.
Soak them in acetone. Acetone will not hurt the coin. Just don't wipe the coin, and if you use a Q-tip, be very careful that you don't add hairlines to the piece.
I am sorry, but Q-Tips don't help with receding hairlines. P.S. It is possible to hairline a coin with a Q-tip. Try it with an inexpensive modern proof. And regarding Q-tips and your forehead, I do suppose it is possible to sloth off dead skin cells in the same way that a wash cloth will.