I'm not a teacher.
All things considered, I am really happy about having had that surgery. (My life is so much easier now.)
If instead of 'having had', you only used 'having' it could mean you're still awaiting the surgery. I also believe that if you provide more context (in brackets), which makes it clear whether you're talking about the past or something that's about to happen, you might just get away with 'having'.
Please wait for confirmation from native English speakers and teachers.