OP, you will have to choose what is right for your dog. May I suggest you let the dog decide. Give up your attachment to a certain death scene. Let the dog tell you what it wants and be open to that. I learned with my elderly dog that you really can tell what the animal wants. I knew when it was time to nurse her back to health despite what others said and I knew when it was time to free her. Her death was so peaceful and so right. Had I made that choice a year earlier it would have felt wrong. The morning she died she was outside enjoying the world. Then she had a stroke and was struggling. When she died it was so right. It's what SHE wanted. I know it.
In the meantime, maybe your dog just needs some supplements to feel better. Or a special diet. Please see a vet to find out what you can do to improve your dog's day to day life. It might not be complicated.
BTW, the "Natural" death you've described seldom occurs in nature. If you're sick you are eaten. You avoid all the suffering. Sure, there's a moment of terror as the carnivore digs its teeth into you, but then your suffering is done and you are free to go on your way (to wherever that may be.)
My attitude about euthanasia for animals is the same as it is for humans...it's a personal choice and it's a viable alternative for those who want it. The first time I euthanized a dog, my (now) husband rubbed my back and said, "We'll do this for each other, right." I am well aware that assisted suicide is legal in Oregon and hope that expands nationwide. Not that it should be used with those who don't want it, but it is a viable alternative for those who do. The thing with animals is they can't tell us with words what they want. We can only watch them with an open mind and try not to put our preferences on them. We have to clear ourselves to their voices.
The only human death I have seen that was as beautiful for the person was in a 2 year old and the only reason it was beautiful is because she was heavily medicated against pain and restlessness AND she was in bed with her parents and died in the middle of the night. Otherwise most I have seen couldn't breathe right (I can't imagine how awful that must feel and hope that the brain is so oxygen starved you're not really around to feel it) or have been incredibly restless. It wasn't peaceful. (Most of those deaths were before hospice so there wasn't a lot of prep or medications.)
Regarding the cost of an evaluation. Our elderly cat looked sick so I took her to the vet. The exam and labwork was a bit under $300. The labwork showed she had lost 80% of her kidney function. She was essentially stewing in her juices. There was only misery and certain death in her future. In that case it would have been cruel to let her keep feeling awful.
When our elderly dog got acutely sick and couldn't walk without a sling around her waist for help, we wrung our hands on whether we should put her down. But she didn't seem ready to die. We nursed her back to health and she had over a year of a pleasant geriatric experience. She still ate, let the kids climb on her, and enjoyed being outside. Then she had a stroke. She couldn't get herself up off her side. She was clearly ready to die. So I did for her what I hope someone will do for me if I'm ever in that state. And that WAS peaceful. I have held four animals (including a chicken) who were suffering before they died and speeding up the inevitable brought peace to them. And each time I cried.