forgetting to register shouldn’t be a big deal. Forgetting to renew your visa is something totally different and can cost you a lot of money. My friend overstayed about 3 weeks and had to pay 10,000 yuan, plus his school also had to pay a few thousand for not registering him.
If you won’t extend this visa again, I’m sure you can skip to register, but it’s probably better to register anyway. If they ask you to pay a fine, then try to walk away and forget about it.