Possible, though you would probably want to come up with a clever way of selling it so that it doesn't look like you're giving a practical gift (which is a huge no-no). Maybe using it as a protective item to keep the 'real gift' from being tainted, and telling them that they can keep the box?
It would however be seen as a definite firm statement of alliance with the Crab, with a subtext of 'we think we're more honorable than you, other Clans'. May be less under the radar than people hope.
Jade Sake box for the Crab?
Everyone gets a small box of sake, with the box customized to each of their interests where we know them?
E: Or just plain sake in artsy bottles, everyone likes booze!
Anyway, since I'll be going to bed soon, and gift choosing takes a lot more thought, I'd vote for the other parts first while the thread hashes out symbolism.
[X] The most skilled in battle
Well, we HAVE sparred with the Crab champion, and then gone out drinking. Our claim to fame was defending the emperor's life.
Thus, the Catfish bringing their best warriors, in spanking new gear with nice big sticks, reminds the court of our heroism, and martial accomplishments.
[X] Bring Boss Koibu. It will hurt not having him at home in Wave Province, but he is completely unobjectionable as a choice of person to bring, and you do sort of want the Emperor to get the chance to meet him.
Bringing Hatsuyuki can leverage on the legendary success of the theater...but this is our first Winter Court. Our objective is to avoid pissing enough people off. Bringing a non-person can be a shocking statement that we can capitalize on while the whole court is confused or the faux pas of the century.
Besides, we praised Koibu to the high heavens to the Emperor. It'd be remiss not to let them meet.