Should I register my corgi's puppies? ?

I have a champion AKC Pembroke Welsh Corgi dog(stud), and an AKC Pembroke Welsh Corgi female. The female is also a show specimen, hasn't done as well as the stud, but she has won. She is about to give birth to her 2nd litter and I would love more than anything that her pups go to companion-only homes. Should I still register the pups with AKC? I had another breeder tell me that I shouldn't register them, and that I should write up spay/neuter contracts when the puppies are of age since I want them to be companions. HOWEVER, I was also told by my vet that I wouldn't be able to sell the pups if they're unregistered and they'll only be worth as much as a mutt. Is this correct? Any input will be much appreciated! Oh, and I sell my registered pups for $550-$600, so what could I sell my unregisterd pups for that's reasonable?