MACs don't involve any key exchange. The ability to share the key is assumed, just like with symmetric encryption. I'd tend to recommend a 256 bit key over a 192 bit key, because the effective key length is halved. 96 bits effective security might be breakable eventually, 128 bits effective security basically never will without discovery of flaws in the algorithm or implementation.
I understand that asymmetric encryption is fundamentally deemed useless under Shor's Algorithm,
This is incorrect. RSA and the usual ECC constructions (ECDSA, EdDSA, ECDH) are breakable for all practical key sizes. Other asymmetric constructions not based on integer factorization (RSA) or the discrete log problem(s) (ECC, ElGamal, traditional Diffie-Hellman) can be secure. EG Lattice-based cryptography (including but not limited to learning with errors, ring learning-with-errors, module learning-with-errors, and module learning-with-rounding), code-based cryptography, supersingular isogeny Diffie-Hellman are all asymmetric encryption thought to be resistant to attack by quantum computers. NIST is running a public contest to standardize some of these quantum-resistant asymmetric algorithms. It's currently in its third round.