Heh, you can do it the Russian way and yank them out while you are awake with just a topical, until your kid passes out from the pain :). That’s how my adenoids came out. Do not recommend.
There's a scene in Roald Dahl's autobiography part one, Boy, that describes the process of getting his adenoids removed without anaesthesia. Sounded terrifying enough that I'm glad we knock people out for that sort of surgery.
I had mine removed with only mild anaesthetics and I still have nightmares about that. It also didn't help with various nose and throat infection at all. In fact I had pneumonia couple years later so not much respect for the butchers that did this to me.
I still have, let's call them interesting, memories of Soviet dental procedures. I think that if I were to put them on film, modern audiences would call them "torture porn".