Warts are a viral infection in most cases, not fungal. You can remove them easily using a sticky plaster and a plain aspirin tablet, sticking a small piece of tablet directly on top of the wart. The salicylic acid in the tablet dissolves into the wart and softens it, so it can easily be cut out after a day or two. Can be painful, but works for those that do not respond well to cryofreeze either because they are too deep or too large.
For large ones you will generally need to have a local anaesthetic injection ( hurts going in, but that is because most doctors do not know how to inject painlessly, Paediatricians learn this very fast. Tip is to first spray a little out the needle onto the skin to numb it, then wait 30 seconds, then slightly into the dermis and a small amount, then 30 seconds or spray the other side, then deeper each time into the desensitised area. Learned that from a combat RN, who also showed how to drop you with an injection as well, but who also dealt with children a lot. She had a few stories to tell) and then cut it out totally and stitch up the resulting hole.