I remember Shin Yodama had his sword's sheath attached to his survival kit or something, so that when he ejected in his first engagement against the Clans, after his PXH bought it, it came with him.
I expect the plan is that they don't go out of their way to use it while in the cockpit, where it's more symbolic of their societal rank, and only expect to have to use it when out of the cockpit for whatever reason.
What always irritated me was the idea the wakizashi was something special Sun Zhang or similar grads could only carry, but that anyone could carry the katana which is, like, the exact opposite of how it worked historically. While I figure cultural drift would be part of it, it's still way more practical to carry a short sword in an enclosed compartment than a long sword - for example, try safely storing a katana in a VW Beetle.
(Edit: seriously, autocorrect, why did you capitalize "cockpit"?)