As far as I know, the only way of claiming ownership legally is by microchip registration.
Legally you have to wait seven days after first notifying him as "found/lost" before you can claim him as a stray and start neutering/microchipping him as your own, and I know you've done everything required to qualify on these grounds.
I'd get him chipped to your address asap to prevent any misunderstandings later on, but I think you're on very safe and solid ground right now.