You have already gotten a ton of great advice and much reassurance, I will add my
I would be interviewing vets in search of one who is familiar with Yorkie protocol. I thought it was just standard procedure to do blood work to rule out liver issues prior to using an anestetic.
Several other considerations are:
1) Be sure that the vet does the intubating and not the vet tech. Life threatening injuries and death can be caused by improper intubating.
2) Unless there are newer safer drugs, Isoflurane is the anesthetic of choice.
3) Be sure that no barbituates are used