The good thing is it is a pre 1974?? boat. How do you know that and how could you prove that, if there is no number on the boat?
I've read about people who steal a current boat, but register it under some old numbers that they pulled off of an old junked boat. How well do you know the seller?
In Texas, I have been told, that any boat without numbers on it is presumed to have been stolen. Current boats, I have been told, always have the serial number on them in TWO places. One on the tag in the back, and again printed or scribed under a seat or the front deck. Looking with a flashlight and your wife's makeup mirror can help find such numbers, if the boat even has them.
If your boat is registered, you may be able to transfer it, depending on the laws of your State. Where are you?
In Texas, you have to come with a clear photo or a scribed record of the imprinted number in the stern. Worse case here is that a TPW officer will inspect the boat to determined if it has been reported stolen at some time. If so, you lose the boat. If not, he may arrange for a number to be assigned to the boat, which may be what happened when the first guy registered it.
A talk with the seller may prove fruitful.
Sorry ....