No computer - data storage solution
For anyone in similar circumstances I can recommend an affordable product that solves both. It's called Kingston MobileLite Wireless G3. It has a 6,700 mAh battery recharger (good for a couple of camera charges), and is able to backup your camera's SD card to a portable hard-drive - controlled wirelessly by an app on your phone.
The device is small (115mm x 80mm x 24mm) and can be stowed somewhere on the bike or in your pocket while recharging the camera. Unfortunately, the power cord and microphone cable both share the same plug, so you can't charge the camera and use the mike at the same time.