Help Request with Smart Key Fob battery

Several months ago I left my keyfob in my trouser pocket, when they both went through the washing machine and dryer. It worked fine, and I have not had any problems until finally the battery died. I believe two of the four screws are rusted in place as I cannot get them to bulge, and in one screw the head is caved out so it is just a cone. Of course the washing maching might be the red herring, and it may have been the other fob that went through the washing machine. I was able to change the battery in my other fob with out problems, and those in another pair of fobs from a friend, so I don't believe the problem is with the screwdriver I have.

Any suggestions?