Based on my experience, it is best to deal in a place that is neutral and secure i.e AP service centre or a friendly gray market shop that you are close with. As much as we would like to protect ourselves, we have to accept that the other party is also wary of us as well. Even cash-on-delivery as a dealing method is not suitable especially where the item is high-value. Best to just accept a bank transfer.
When selling watches these days, both the buyer and seller face challenges, hence the reason grey dealers are popping up like mushrooms.
Buyer would want to know the item is genuine and probably wants to have the caseback removed to check the movement.. a secure environment to perform this as well as to perform the transaction if bringing cash. Then he/she wants to be able to walk away from the location without being followed or robbed after. Then there is that guarantee that it is not a stolen item?
Seller would want to be sure the buyer is not a conman who wants to run away with the watch or bring a bunch of friends along to rip it from your hands. Being conned by fake online transfers or floating bank balance means one is not prepared to sell online.
I'm not sure if I'm allowed to disclose the details of the scammer here without any legal consequences. Otherwise I'd gladly name and shame the scammer.
I'm sure we would all like to know if said person is a member of this forum. Maybe the mods would be able to share if exposure of alleged scammer is allowed.
You have made a police report.. hopefully the police do actually try to track the person down even if no crime has been committed yet in this case.
BTW, you should already have been suspicious if your watch, which is not a full set, at this asking price had actually attracted anyone..