What does the seller say when you ask for the serial number? Are they not replying? Flat out refusing? Claiming they don't know where it's located?
You could tell them straight up that without a serial number, you're not interested.
Just curious - what does the serial number tell you, anyway? It would be pretty difficult to steal a longarm, they're quite heavy and awkward.
Another thing - if you're nervous about the cash, insist on using an escrow company.