I spoke with my anesthesiologist
and he was great
and said he would use the smallest tubes possible
and I did not have the same issues as I had during a different surgery....so, it is possible to speak with them and let them know what is going on with you, and it is in their best interest to know about these issues ahead of time.
If your Dr knows about these issues he should take precautions and let your anesthesiologist know...