Why not use veterinarians? They can access the same drugs (although not human grade, but I doubt that would make any material difference). And vets aren't as-a-whole barred from executing animals when deemed necessary, so perhaps the ethical quandary can be sidestepped.
What if the vets don't want to be used? Anyway, I'd guess, since some medical professionals can and do assist with executions, vets probably could too.
Are they legally allowed to treat humans in USA states?
ETA: Apparently not:
https://www.successinveterinarypractice.com/veterinarian-treat-human-medicine/
Interesting; they can in the UK, but doctors are not allowed to treat non-human animals.