And neither, I think, does anyone else in Gensoukyou, for that matter. Maybe you should ask Yukari; she’s definitely the most up to date on… well… anything really. It was through her that I got this computer, y'know.
From what I understand, a surgery involves a doctor cutting into the body to modify something inside, yes?
Given that this is the case, I don’t think it would actually be possible for me to even have surgery, as my humanoid form is just a visible manifestation of the spirit occupying me. I mean, I’m not intangible, but if I were to sustain serious injury I could just disperse and reform, good as new.
I hope this has helped shed some light as to how tsukumogami bodies work!