The best person to talk to would probably be your agent for general insurance (non-life). I had taken the All-Risk Insurance previously, and the premium was on the higher side at 25% of insured amount, IIRC. 4 years of such an insurance and you would have paid for a subsequent piece, although you do get peace of mind during that period. Back up the value of your insured article with documentary evidences of purchase and/or valuation.
A cheaper longer-term option... would be to invest in a fire-proof safe. And if your watch winder could run on battery too (besides direct), you could place the winder with watch in the said safe, and the watch is good to go with the correct time anytime you so pleases. From personal experiences, I find the Chubb Mini Banker a good safe if your collection ain't too extensive i.e. it could accommodate standard-sized watch winders. Just my 2 sen.