If you are only spot cleaning, then you don’t need to remove your bp. One method you could do is cover their head gently with your hand, coming from the back side. You should find that your snake will ball up. I would do this and place them either back under their hide, or keep your hand over top until they relax.
If you are deep cleaning, or moving the enclosure then I would recommend using a snake hook if its too scary to move your snake with your hands. If the paper towel method works then that’s great, otherwise a snake hook works fantastic. You could also place them in a pillowcase to keep them calm.
No need to bump up the humidity higher. Ideally it should be about 60-65%. I would recommend a low wattage heat bulb to keep your cool side temps up. If it’s 80 normally, and dips to 71 at night then I wouldn’t actually worry. Some variance like this is not a big deal since, naturally, temperatures and humidity will dip during the night(personal preference). But if it is periodical for say a day or two then I’d definitely invest in a heat bulb.