Stolen rolex advice

[rolex3301]

Hello I had recently my watch stolen in armed robbery as I was walking outside of a club, the problem is that couldn’t go to report it in the police as I didn’t had the serial number, the box was in the bank safety box I have in Swiss while I live in London, anyway I got it after 1 month so now I finally went to the police and have the paper with the serial number. The question is

Should I go to Rolex to report it so to out the watch in red list or better let some months to pass so someone goes to Rolex to authenticate that is not stolen so the new owner after sometimes go to service and then block the watch ?
I mean if I go to report it now the thieves wouldn’t be able to sell the watch
I mean they have access to the stolen watch serials so they know if a watch is reported as stolen or not….

What do you think