Better than my suggestion is to imagine how your might play with the magic of directly harnessing EMF to communicate, then to use search terms such as ARRL QRP CW 50mw backpacker rig transmitter transceiver amateur and so on to find something that is right for you.
I built a matchbox-sized cw transmitter that can use from 5 to 20 volts supply using about $20 worth of parts to produce filtered cw at about 50mw at a crystal controlled 14030 MHz into whatever antenna that you can match to the output. I bought the tiny circuit board mail order and populated with a handful of discrete parts bought from a local Radio Shack (R.I.P.). Took about two hours. The code "key" is two pieces of twisted bell wire that can develop good speed with, surprisingly. You have to use this rig with a separate SW receiver. Any reasonable quality one will do, such as one in the Sony ICF family. A "CW" setting is not required.
Many kits are transceivers, so no additional receiving equipment required.
Depending on the match of your antenna and the ionosphere, you can get QSLs from hundreds of miles away. It still gives me the shivers to do this miles away from civilization under a dark summer night in the mountains. Such a tenuous connect, such an achievement harnessing one of the basic forces of nature to exchange thoughts at a distance.
A Lithium-Ion power density and weight makes it an obvious choice for powering your xmitter.
Neal Stephenson's scenario in his new book Seveneves of cw contacts to the ISS is completely possible.