I have a similar problem.

I buy corn removers, like this. Get the cheapest ones but make sure they have several salicylic acid disks (compare how many salicylic acid disks they have, that's all you want).

If your warts are smaller than the size of the disk, you can cut it to the size of your want.

Put the disk on top of your wart and keep it on with a band aid, don't use the things to hold the disk on that come with them.

Since it is on your hand, I recommend these waterproof band aids that don't come off when you get your hands wet.