If you think that may be too rough such things can be cleaned in the dishwasher on the bottom rack topside down and opened. Turn off the drying cycle. Bad dirt spots can be soaped and brushed before running it through. This works on ballcaps that you don't want mushed up in the wash too.
I actually preferred my F2 after I washed it, it was more pliable and comfortable to carry. I did spray it with some 3m waterproofer too. I may do the same with my newer F1 to break it in.
For a canvas bag, I would wonder about a self-serve car wash pressure washer. That is what I do with old tennis shoes.
Our clothes drier has an attachment shelf so that you can set shoes or other items in the drier without them tumbling around and they dry from the heat.