That alcohol percentage in whiskey is high enough that the alcohol would slowly eat away at the cork. To make sure the cork doesn't dry out it is best to keep the bottle upside down for a few seconds once every ~6 months.

I've been using the logitech marathon m705 for the last 10 years for that exact reason. It doesnt have rechargeable batteries but the AA batteries it came with lasted me for almost 2 years. Now, even if I buy cheap batteries I know I don't have to worry about it for at least another year.