Yea we also handled it ourselves the first couple years but it was so painful. Literally the same thing you described happened - as well spending weeks+ how we need to file it as tax when we pay bounty to someone in Pakistan etc.
Are you in the US? You simply collect a W8 from them that you keep on file and then the payment would be counted as an expense on taxes. We do payout to hundreds o f affiliates every year and this is how we handle it, it's really not complicated. The actual payments are done via Wise batch payments which just requires their email address.