I have had success with using 9% hydrogen peroxide. It was the standard stuff from a chemist/drugstore.
Not too strong to burn too much but you do need to file the skin on the surface of the wart before application for it to work well.
It has little effect on healthy skin and bubbles like mad on the wart itself. It did still sting a bit.
Application something like 4x a day did the trick but did take a little over two weeks. (but less than three).