un-neutering a dog is impossible as without the testes no sperm and they actually remove them. same with a female, everything is removed, unlike in humans where its just basically 'disconected'
as for choosing the bitch you stud to, that is completly YOUR choice, you want to better the breed and that is wonderfully admirable! ive lately seen alot of adds from people looking for studs, most along the lins of "looking for a stud for our purebred 9lb chi, she doesnt have papers but is "pure"" and alot of adds VERY similar to this, these are the people that give breeders a bad name, and if every breeder with a stud refused to breed with unregistered or 'bad' examples of the breed them wed progress to continue to improve the breed!
I commend you for using your best judgment and refusing some breedings.