I would like Dodgee or Doc to agree, but all the suzuki gearboxes I have ever seen have the gear shift shaft running right through the cases.
To replace the shaft you remove the clutch side case, then the clutch and basket and then you can simply slide the shaft out from that side.
I would have to take a look at one of my engines, to confirm. But I am 99.9% sure you don't have to split the cases.
Good luck finding a good runner…