What do I put down as the reason why I need to be out of work for 6 weeks?

As for the Mexico part I think most people would understand that many surgeries are cheaper there.

You might not need 6 weeks depending on your job but it isn't an unreasonable time to ask for. I work at a computer and while I could have worked from home the first couple of weeks it would have been torture to drag myself to the office the first 4 weeks.

If you have to tell I guess my feeling would be first HR and ask for their discretion. If it is a small company I would sit with my manager and talk it out, again asking for that persons discretion. While there can be idiots in either case, I found people were usually pretty good at keeping it to themselves until I was ready to talk about it.

Pete