First, what you want to do is done every day, more than once. Sold my father-in-law's car for him without him around or being in state. Title signed already.....no problems.
Don't know about NJ, but in MA, GA, SC and other states, the plates remain with the owner/registrant of the plates and typically have to be turned in to the DMV. I know in MA the plates must be turned in to cancel your insurance.
For the buyer registering the car, you need to go nowhere and do nothing. Once you sell it, hand over the signed title, bill of sale, etc., and get your money, you're done with the transaction. The onus is then on the buyer to get it registered.
If you want to go all out, get a Power of attorney form online, have him fill it out, and GF notarize it. It'll allow you to do anything you need to do title wise if there are issues. I did it buying a house recently, and its easy to do. Generally you'll then sign 'His name by your name, his agent.'
If you go the power of attorney route, and I wonder why you'd really need to, get a limited power of attorney specifically for selling the car. (A general PoA would potentially give you the ability to do darned near anything with your father's worldly goods, and then some.)
Then you wouldn't need your father's signature or anything else--you'd do all the signing, etc. You'd have to attach a copy of said PoA along with the title, and I'd think whoever bought the vehicle may have a more difficult time getting it registered instead of simply letting your father sign the title and you sell the car. Heck, bet you even have your father's phone number and can talk with prospective buyers.
