Their website says they do but you can't be present. Their prices are comparable to what I have paid vets in past. Please consider that option so you can be with your dog rather than them being afraid.
You can call them and talk about it, since they can't do vet exams for the public you technically surrender your dog to the shelter and they will euthanize him and give you back his cremated remains. The downside to this is that you won't be able to be in the room when they perform the procedure. So sorry for your loss, hope this helps.
Usually your veterinarian would see you through this.... Call Seattle Humane Society... I don't know what services they offer but will surely head you in the correct direction... So very sorry to hear about your pup.... 💔
Thanks! Your answer is awaiting moderation.