We flew home on Day 12 post-op with no problems, other than weather delays because of storms all over the country ..... that was a bummer and I was exhausted when finally home, but no health issues because of it.
We flew United using frequent flyer miles on non-refundable tickets. We were told by House beforehand that they have the forms to fill out for a medically necessary change, should that have occurred. You may have to pay a "change ticket" fee ..... do not know about that. If I were you, I would call the airlines you plan to use and specifically ask if you can change your flight with a medically necessary form from your doctor and if so, how much it would cost.
We deliberately chose 12 days post-op, even though House said I could fly 10 days post-op. I think I could have flown on day 10, but I really felt considerably better by day 12 and glad we planned it that way.
Hope that helps.
Clarice