The way it should work is that you contact customer support to confirm that the transaction is okay to do, then agree a payment method.
Once APAT agree the transfer, you can part with your cash. Transfer via Stars or FT would seem the cleanest way to do it.
There shouldn"t be any problems then and it is kinda self policed. To have won a seat in the first place, APAT must have the guys details and will confirm he has a seat to swap.
Seems full-proof, famous last words I know, but you should be fine.