I recently lost my beloved old dog suddenly, at home. While we believe it was quick and painless for him, for which we are thankful, it was very traumatic for us to see him die - his body going through the throes of death, not in the 'going to sleep' way that happens with euthanasia. Like yours our dog had slowed down a lot and tired easily, although he was still enjoying food and short walks. Afterwards, I was visited with inevitable regrets that I hadn't known he was in his final hours that morning, and if I had I would have tried to make things more special for him and of course said a proper goodbye.
In contrast to this, I have had two elderly cats PTS and while it was horrible to fix the point of their death, I was able to make sure I had said and done everything I wanted. Also, the grieving process started as soon as arrangements were made, whereas with the dog it took time to even take in what had happened and we were completely knocked for six, and left with the awful task of dealing with his remains and keeping them at home as it happened at the weekend when the vet was closed.
The point I am rambling towards is that having had experience of both I would choose PTS as being best both for your pet and you and I would not want to risk a natural death by leaving this too late. You cannot be sure that a natural death will be quick and painless, and with PTS you can prepare yourself. I would talk to your vet (may have to be by phone) to see whether they think it is time.
There is no easy way - I hope you can make a decision soon 
.