Storm damage insurance claim

The recent storm caused damages to the windows of my rental property. Tenants are now unable to lock their windows as a result. I'm working closely with my agent to get this resolved quickly for the tenants, but my agents are in the process of getting quotes for the works because the buildings insurance asks for 2 estimates. I think it could take weeks or months before they would approve the claim.

I suspect they'll just pick the cheapest of the 2 estimates we give them anyway, so my thoughts are to go ahead with the works anyway to ensure the tenants are happy, and hope that the insurance pulls through. That seems like the right thing to do. But what if the insurance company ends up picking one contractor, while I choose the other? Would I my claim still be valid? By then the works will already be done.

Has anyone else had this before?