Any vet should be able to perform euthanasia on any animal, what’s important is to render unconscious first to not extend suffering. Any vet with gas anesthesia can accomplish this with a mask or chamber and slowly turning down the % of oxygen in the gas delivery. You can actually overdose animals this way and accomplish euthanasia, but a vet should always follow up anyway with a stethoscope or injection if necessary. I worked as a vet nurse for years and we euthanized a lizard (ziploc bag chamber as he was small) and small furries would be the mask or chamber depending on what least upset them. I had to have my pet cockatiel euthanized, but I took him to a different vet as I couldn’t watch and they returned him to me for burial. He looked completely peaceful and unruffled, so I assume they did a similar process. A good vet will be compassionate to the owner and the animal, even if not a type of animal they usually see/treat.