If your main goal is to hike and to document that hike with some memorable pictures, you should take your phone camera. You mention that the last camera you used was a digital Canon (presumably point & shoot) ten years ago. The cameras in today's high-end and medium-level smartphones easily surpass that of digicams of that era. And, the results will be comparable to today's "tough" compacts.

The main drawback is that you'll have a fixed focal length lens — no zoom. But, phone cameras generally have a very flexible medium-wide lens, and these days, enough real resolution that there's plenty of room to crop.

Presumably, you're already taking a phone. That means that additional the weight and size is zero. That's going to be very hard to beat.

But, if you really are thinking of this is as photography trek, and you want to learn photography, you should budget a good chunk of your weight and trip planning to photo gear. In this case, all of the advice in Are there disadvantages to a prosumer camera for a beginner, aside from cost? applies. I definitely discourage using one of those "tough" compact cameras — the technical image quality won't be significantly better than you'd get with your phone, and you won't have the advanced control you need to get good results.

As much as I like the low-tech suggestion of taking a film camera (maybe even one which works entirely without batteries), I really can't agree in this case, because it's not a very good learning tool without a feedback loop. To learn photography with a film camera, you need to develop very frequently and evaluate your results. You won't be able to pack a darkroom, so digital is better. If you do decide to go this route — and it's not completely crazy! — make sure you're very comfortable with your camera and your ability to make good images with it before you set off.

Several companies make chargers specifically for camera batteries. Voltaic Systems is one of them — in fact, they make solar backpacks. Assuming you're in good sun, the medium size of these should charge a mirrorless or DSLR battery in five or six hours. Bring two or three spare batteries and charge them when you can.

I personally would recommend one of the smaller Fujifilm, Sony, or Olympus mirrorless cameras. Or maybe even something like the Fujifilm X100F — nice and compact with a fixed lens. But you won't go wrong with a DSLR, either.