These batteries are definitely rechargeable and if you have one of those oral B rechargeable toothbrushes, simply leave your key positioned in the charging base for a day or two and this should recharge the battery if the battery is still functional. This worked for me on my spare key which I never used for a long time. The charging base of the toothbrush is made entirely of plastic with no conductive metal and charges the toothbrush in the same way as our keys apparently get charged when in the ignition. This may be worth trying before cutting into your key.
Great DIY write-up to the OP and all others.