This experiment by CBC that used chirp over the radio to transmit a wallet seed tickled my interest. Of course this isn't secure. And it's also inconvenient to create the wallet from the seed. What's a better way to do this in a practical way? Chirp is very accessible and convenient. Shortwave radio has a decent range, some distance over the sea.
Although I am not qualified enough to suggest a protocol for over-the-air, I can still get some technical pointers. You may want to ask at the ham radio SE community.
Yes you can easily send Bitcoins over shortwave radio using encryption but radio encryption is not a topic of this community. It's also severely illegal in the U.S. for a HAM operator to use any kind of encryption when transmitting.
The Bitcoin network over-the-air
This is what I think you are asking, the Bitcoin protocol does not send private keys of bitcoins around as its main technique as this is risky and dangerous inherently. The Bitcoin protocol moves bitcoin without the need to exchange private keys of any bitcoin so it be better to just implement the network over radio.
Bitcoin can practically be agnostic to the protocol you are using, as long as communication is possible Bitcoin will work. There are many protocols for shortwave radio available that can move data from a transmitter to a receiver. As an interesting example, you could totally set up a node that communicated via Morse code as long as it has other nodes to talk to. You'd run into problems with bandwidth as some tx/rx modes are slow. You can possibly use a modified version of Bitcoin-qt and use the same handshakes and messaging it does over tcp/ip.
The HAM radio community has interesting an P2P by itself which you can look into. APRS is a packet-based network which relies on peers to rebroadcast messages, it's really cool and is readily documented and has many tutorials.
I've been looking at this question too. It is my understanding that a bitcoin transaction is not "encrypted" . The information is not obscured in any way, and can be transmitted publicly without breaking the security. You are simply transmitting a "hash" of the transaction, or signature. Nothing has to be decrypted to be read. You simply verify the signature to see if it is a valid transaction. It's not a big deal for everyone to see the transaction itself. They will anyway once it's in the blockchain. My best guess is this would not break the obscurity rule in the US.
The rule I think that might be in play is not using amateur radio for commercial purposes. Buying an item through packet radio would most likely trigger this limitation. What I wonder, though, is if maybe it could be used to send some sort of humanitarian aid, for instance if one person with bitcoins does not have Internet access, and wishes to send money to someone who does, via radio. I can't think of a way a person could 'receive' bitcoin without being connected to the Internet (since receiving is really only recording the transaction in the blockchain)