As far as notification if something goes badly (hopefully it won't be a concern), just make a list of who should be notified and give it to whomever is closest to you. My wife and I have that anyway... our "In case I get hit by a bus" documents.
I have taken time off for surgery before, and based on my experience, I have one more bit of advice - forget about work for a while. Just worry about your own recovery. Stressing over a job isn't how you should be spending your energy during a time like this. You'll know when it is time to start thinking about it again - there comes a point during recovery from major surgery where you are tired of recovery and want to start doing something again. That is the time to start thinking about work, not before.