While all your shaving paraphernalia is great at home, you don't need nearly so much. If shaving on the trail is important to you, and you want a lighter kit, try this:
Razor: Disposable, plastic handle and head.
Soap: Dr. Bronner's or whatever you prefer to bring.
Process: Heat some water to your preferred shaving temperature, splash it on your face, or use your bandanna to soak your face. Squeeze some soap into the palm of your hand, with a tiny bit of water, then use your other hand to make a lather. Spread the lather on your beard. Dip the razor in the hot water, and have at it. When you're finished, rinse your face and razor with the remaining hot water.
All the rest of your kit is just fun accessories, none of it is actually needed to shave.