Nothing wrong with asking a cop friend to run a number for you. The catch is that if the gun comes back stolen, he had better be able to produce the gun. You will have to actually have the gun before they will do this. Running the number for a gun that they do not physically have in hand could cause problems for them if it does come back as stolen.
I've done this a few times with guns purchased FTF. You will lose the gun, but I'd not want it anyway. Better to lose a little money than have to explain things to a judge later. Having the name and address of the person you purchased it from will help you get your money back as well as proving you did not steal it.