All surgeries must be done on a sterilized environment.
But there could be some kind of transparent gel, that would be antisseptic (or at least innocuous). Then the surgeon could, for instance, open your chest, fill it with this gel and do the work. It would look like a mess, but the gel would greatly
reduce the risk of infection.
When the surgeon finishes his work, he would remove all gel that he could, and what remained would be absorbed by the body.
The only major drawback that I can imagine is that even if the gel is transparent, it would distort the view of what the surgeon is doing. Well, since this is all speculation, this gel could also have the same refraction as air, and would indeed look like air. Aerogel? :)
But even if the gel distorts the view, I think this idea could be used on emergency situations, in a war for instance, where sterilized environments are extremely rare, and wounds very common.