16 bit (2 byte) Digital Signature
TLDR: Can't do.



16-bit is simply not enough for digital signature, which requires many times more bits¹, and can't be checked if truncated (becoming useless).

One may want to consider a Message Authentication Code, such as HMAC with SHA-256. At least, that's cryptographically better than an encrypted CRC². But there must be a shared secret between sender and receiver(s), thus that's not usable in the question's stated context.

If one absolutely needs public-key verification, the only option that I see is signing a group of earlier packets in a special signature packet (or group of signature packets), as the question proposes for "critical information". Problem is that losing a single packet prevents verification of the signature.



¹ To attain even mild security (80-bit), the most compact signature schemes around require about 224 bits (or 160 for a BLS scheme once used but now thought quite vulnerable), for something that is added to data renaming in clear; or down to 64 bits if you accept that about 1200 bits of the payload remains scrambled until cryptographic verification (even though only the public key is involved for the unscrambling, it's very debatable that the later meets the requirement of non-encryption in amateur radio).

² It is trivial to alter a message without changing the CRC, thus the encrypted CRC.