First off, I'm so sorry you are going through this. It's rough seeing our pets get old and feeble. Someone once said the only fault of dogs is that they don't live as long as humans. I tend to agree. It sounds like your dog has had a long, happy life with your family. To live 18 - 19 years, I'm sure your pet has had wonderful care, and reading your post -- you're faithfully standing by him to the end. What a fortunate dog.
Ultimately the decision is up to you, but I have to say, if you think he's suffering or in pain, certainly putting him down can be a mericiful thing to do. Also, I think you'll know when it's "time". Your wife has expressed that she feels it is time, and maybe in the morning you will feel the same way. Being at the vet during my dog's last moments was actually a beautiful thing. We loved that dog so, so much and I think he understood. It was very peaceful for him and the vets were very respectful.
Whatever you decide, it will be okay. I'm not sure about St.Marys County, but I do know there are vets that do make "house calls". Maybe someone else here would know more, or you could inquire over at the dog forum area. Anyway, I know someone who had a vet come to their home to put the dog to sleep and she really appreciated having the house visit versus taking the animal to the vet -- it would have been too stressful for her and the dog.
I also know someone that struggled with the same decision for their 19 yr old dog. The afternoon that they were going to go to the vet, they found their dog peacefully passed away just a few hours earlier.
Again, so sorry you are going through this, and hope a restful night may bring some more direction for you in the morning.