My stepson has AS (and he's had surgery) and I am a nurse so my response comes from both of those experiences.
I think the best thing that can be done would be to work with the child life specialists ahead of time to make up a social story (with visuals) ahead of time that can be used and referred to before and during the experience. Many child can adapt to the different ways adults explain things... but kids with AS will struggle with this. It is important to inform them, but not make it overly specific, because as/if things change it might be very difficult for them to adjust to those changes. I would encourage the staff to use the same descriptors/language as the social story to keep things consistent.
Also, a lot like older adults, they do not behave the way you would expect when they are in pain and may not be able to use a pain scale the ways their peers would. I would watch more for agitation and restlessness than reports of pain.
Other than that, I think many children's hospitals today are doing things that would help as AS child... like allowing parents to stay 24 hours and be in procedures, and be allowed to eat what they want (when eating is allowed).
I don't have a lot to offer about classic autism, hopefully some others will chime in with that. HTH!