BP Bad Shed?

So I'm a first time snake owner, and I've had my baby ball python for a little over a month now. Two days ago, he shed off the skin on his head perfectly fine, but then he stopped shedding when it got to his neck. It turns out I had a cheap hygrometer from the pet store (I need to order a better one) that was reading the humidity wrong. He still has not shed the rest of his skin, and it is starting to look wrinkly. I hear that I should soak him in some warm water and try to help him get it off, but I'm not really sure how to go about that. He is still new, so I don't to spook him. Sorry if this question has already been asked, I'm just concerned for my little boy. What should I do?

Fix your husbandry and the proper humidity will help remove the shed.
You can try putting your snake in a damp pillow case for a little while.
The problem everyone forgets with soaking is that you are also washing away the oils that are needed to shed also.

I'm working on fixing the humidity, but will my snake be harmed if he leaves the skin on for too long?

I'd raise the humidity and wait to see if he can get it off himself. Soaking can be a little stressful sometimes, and as Pit said, it can rub oils off. You can get some sphagnum moss, get it moist, and spread it throughout the enclosure (or in one hide, which is called a humid hide) to raise the humidity. Misting will spike the humidity temporarily, too. What sort of enclosure do you have? Tanks are known for having humidity issues, but people have posted some tips on successfully keeping up humidity in a tank (such as putting a damp towel over the top, covering part of the top with foil, etc.).

Also, this is a good, cheap digital thermometer you can switch for the analog one (if you haven't found one).

I have a terrarium with a screen top, and I'm trying some of the techniques people use to bring the humidity up. Also, thanks for the hygrometer I might try it.

I have used those Acu-rite therm/hygrom and they work well. I used to keep one in all my tubs.