Let me add my 2cents without experience for special luggage.
UO is a LCC and the rules for non-CX OWE or J pax connecting to/from UO (even with CX codeshare) have not been generous.

Let's assume that you have a return ticket from Japan with a UO regional segment.
My guess is that they will check-through your bike from Japan. Hopefully you won't have to pay the UO special bag fee.
I would be much more doubtful on the return. UO can check it though but might require to pay their fee. My (poor) experience with UO is that they try to milk you anyway they can.
Personally I would not worry about interlining bags on a CX ticket, but the fee to be paid is the only issue. Arrive early at the airport.