The explorad or the input device must contain a power supply. As the whole device will be mobile, I need to charge it without too much hassle. While the explorad should stay mounted on the telescope, the input device can be detached.

If the input device contains the LiPo battery, it's probably easier to charge the battery. There are small charger ICs for that purpose, and I even found an example of a circuit that uses the MCP73831 and provides load sharing - it can charge the battery from USB and at the same time supply the load:

http://blog.zakkemble.co.uk/a-lithium-battery-charger-with-load-sharing/

As the load requires 5V, I will need a step-up converter. They are readily available as small modules. Furthermore, the Teensy 2.0 can be used to control charging and send status information to the main device.