I’m sorry you’re dealing with this decision, it’s tough even when we know it’s the best thing for our beloved animals.
I emailed my vet when I made the decision to euthanize two horses this summer (two unrelated, irreversible, painful medical conditions) - as I knew I’d burst into tears trying to talk over the phone. They were very considerate, did not question my request or push for further examination, just gave me a few available times so I could see what would work with the removal service they recommended, and took my credit card over the phone so I wouldn’t have to worry about that detail on the actual day. When the Vet was running late for the appointment due to an emergency, he even called to notify the removal service so I wouldn’t have to. Day of, the Vet and assistant were incredibly compassionate towards me and my horses, and the removal service treated their bodies respectfully.