The work has clearly been done to an unacceptably low standard & the customer is entitled to be compensated for this. Some information is here:
http://www.adviceguid...ervice_done_badly.htm
It gives an example of a dress being ruined & says the customer should receive compensation - the amount taking into considration the age & condition of the dress. Using that principle, your customer may or may not be entitled to a new watch. Clearly, the ruined watch is far from new so it may well be that its value is less than a new one, & if that is the case then compensation amounting to its present day value would be reasonable. However, it is a limited edition watch, & I have no idea whether that means its value has not declined in the way you would normally expect. It could even be worth more now than when it was new!
As you can see, this is not easy to resolve. You need an expert to value the watch in the condition it was in before it was damaged, & you then need to decide based on that whether to agree to give a new watch. If you decide not to do so, you have to negotiate with the customer to try to find a conclusion which he will accept (such as a contribution of £x towards a new watch).
All of this is fraught with difficulty, & the customer could refuse to agree anything & start a Court claim. You would then have Court costs & could end up with a far worse situation than just giving him a new watch now. If you do give him one, you will at least have the likelihood of a customer who is not entirely p***ed off with your firm; if you make it too difficult he could easily lead other potential customers to shun you.
I assume your boss must have some good reason for not wanting to make a claim against the repairer, because he is the person who should be paying - or his insurer should.