I would just say this. What a human wants is most likely not what a pet wants. The only thing your pet know is it’s humans. That’s where they get their comfort and security. To die alone would be borderline cruelty.
There is no reason to put them on a slab. Do it at your house. The animal will be more comfortable and so will you. These animals don’t feel pain when correctly euthanized. They just literally go to sleep.
That’s all I’m saying.