I think a Cashu token is more like a one-off federal reserve note. It's a bearer instrument backed by a mint instead of the Federal Reserve. A letter of credit would be more like a certified letter attesting to one's wallet balance, thus providing proof of ability to pay.
Discussion
It doesn’t attest a wallet balance. It it simply a promise to pay on behalf of whoever the bearer is. Letters of credit were a precursor to standardized bank notes.