First of all, you mention the TCP/IP checkum, at the same time as key exchanges, long PSKs, and money transfer. Which is it, simple message integrity or message authentication? If you need authentication, you shouldn't even be mentioning TCP/IP checksums. If all you need is integrity, then just append an MD5.
Assuming you need authentication: I don't have any opinion on Blake2, but you should use an HMAC instead of just appending the shared secret key and taking the hash. HMAC can be built on top of any hash function, including Blake2. You should also make your MACs at leasts 128 bits long, preferably 192 or 256. 64 bits is definitely bruteforceable these days. I wouldn't settle for anything shorter than 256 for a protocol that involves money.
Keep in mind that a basic message authentication code is only one piece of a secure protocol. There are many possible attacks that might slip through (e.g. replay attacks, MITM, timing attacks, ...). For example, you need to ensure that an attacker can neither reinject a message from the current session back into it (e.g. by using a sequence number in the signed payload) nor reinject a message from a different session (e.g. by ensuring that there is a random component to the shared secret) nor somehow guess the right MAC code (e.g. by making sure that the wrong-MAC responses do not leak any information, neither in contents nor timing), and of course there's always the host identification problem (preventing a simple MITM where the attacker performs a key exchange with both sides and resigns/reencrypts traffic both ways). Honestly, your first choice should be to use an existing well-tested protocol, such as TLS (you can build your own host verification rules on top of it, you don't have to use the "well-known" root CA list). Failing that, consult a real crypto expert.