A Suzuki shop should be able to tell you if you can just change the seal from the outside or not. If it is anything like the kTm countershaft (sprocket) seal, you should be able to remove the shift lever, pry the old seal out, and carefully tap a new one in its place. Be sure to clean the area after you remove the old one, and run a very thin coat of plain old bearing grease around the inside of the new seal (the rubber, sealing part) with your finger. Tap it in place with a socket and a rubber mallet (or any hammer). Drive the new seal in square and don't drive it in too deep. Take not of how the old one is positioned before you pry it out.
In the pictures below, you can see the shift shaft seal below the countershaft area. Some seals have a flange so you can only drive them in until that flange contacts the case, and that's it. Notice on the countershaft seal that there is no flange. That is why it is important to take note of how far it is driven in before you remove the old one. Also note that while the metal ring on the seal looks like a thick, solid ring, it is in fact hollow, or "U-shaped", so it is more fragile than it looks. This does make them relatively easier to remove, however. But, be careful not to bend or crease the new seal when installing it or it will not work!