I'm willing to bet most of these issues are more psychosomatic than as a result of a dip in hormonal levels. This is probably something you should talk about with your physicians. It takes a while for a drop in hormone levels to actually start causing issues, because hormonal fluctuations in the body are normal, the body is accustomed to it. If you are noticing an issue after a day or two, that's certainly a psychosomatic response, your brain is saying "oh no! oh no! The testosterone is coming! The testosterone is coming!" It's purely an anxiety related psychological response that probably has nothing to do with an actual hormonal deficit.

On the other hand taking HRT before and after recovery from surgery is unlikely to cause any issues unless you have other risk factors like obesity or heart disease, discuss your issues with your surgeon and they may be willing to make a compromise.