photo 2011 Chris | more info (via: Wylio)
How should you tactfully ask a vet if he / she has experience with Greyhounds? As you well know, physiologically they are different from other dogs (PCV is higher, WBC lower, etc.) and a vet without this knowledge could be dangerous.
You forgot to mention that Greyhounds are prone to excessive bleeding during surgery, that they frequently experience rough anesthetic recoveries, that some anesthetic agents (barbiturates and, in my opinion, ketamine) should be avoided in Greyhounds, that some Greyhounds metabolize sedatives at extraordinarily low rates (I am aware of a Greyhound who acted drugged for four days after receiving a medication that was supposed to last three hours), and that their skin will lacerate if it comes in contact with anything that is even remotely sharp.
Greyhounds (and all sighthounds, including Whippets and Italian Greyhounds) definitely require special consideration at the vet’s office. Most of the vets I know are acutely aware of this. Most experienced vets have experience with Greyhounds. But I will concede that in my day I have seen a few vets make some pretty big Greyhound mistakes.
There is only one way to find out whether your vet is Greyhound-ready. You need to ask him or her. Be polite and non-confrontational, and just ask. A good vet should be perfectly happy to discuss his or her qualifications. If your vet is offended, you should look for another.
That said, be aware that most Greyhounds actually do not suffer a catastrophe when they go to the vet. I have treated hundreds of sighthounds. During that time I have seen one who suffered unexpected bleeding during surgery, and one who suffered from a large laceration when he brushed against an exam table. Most of the time Greyhounds do fine with sedation, anesthesia, and treatments.
Don’t get me wrong. I always exercise extreme care when working with Greyhounds. But I do that with all of my patients. I, like most vets, take my job seriously. And I, like most vets, always am happy to discuss my experience and qualifications with any client.