I'm so sorry for you and your frog
For the 'surgery'... I've seen home surgeries successfully performed on goldfish using clove oil as an anesthetic. It's tricky, because clove oil is also used to euthanize frogs and fish. So you might not want to try that unless someone has any ideas for dosage. Just tossing ideas around. Sad as it is, I would recommend having some clove oil on hand anyway in case things start to go bad. Hopefully it won't come to that though.
It might be good to find a partner to help you. Maybe someone to hold the frog still and keep it from injuring itself so you can have both hands to work.
Good luck, and keep us posted! I don't post often, but I stalk the forum a lot and I've been watching this thread and sending you guys good vibes since it came up!