Ted,
It works like this....I know someone highish at Heathrow customs. And the procedure is always the same, although it has relaxed a bit due to terrorism etc.
You get spoted. There are people out there trained to do just this. If you paid for the watch via credit card even worse...don't belive all the mumbo jumbo about privacy and data protection and you may well not even get stopped if you paid this way as there is clear proof you bought it. So...you are spotted and perhaps even searched...nothing...you have posted the box say in New York back to your home addy...the second the box hits customs (they are looking for it by the way) bling, visit from customs and it wont be just the tax they will be looking for.
There is one way around this or two....box gets sent to a mate and paperwork to another, or they both disapear. If ever questioned about the watch.....a present to a good friend in the per say usa. And yes, similar to the one you are wearing. They have to prove it is the one you bought, wont happen.
As for insurance...get a snap of you wearing the watch plus a couple more in detail of the item itself. And make sure you keep a leaflet etc of its cost new....in case it goes missing insurance will want proof that A you had it B how much it costs, IE not that you necessarly paid for it as anyone can insure a gift.
Hope this helps, Snoopy