If the Shimano Sl-8S20 Revoshift is made like their other Revoshift twisty grip shifters it isn't really user serviceable. Everything snaps together with plastic tabs, the cheapest possible form of assembly and it's designed to be a one-time only process. When components like that fail they're usually replaced rather than serviced.

Without great care to avoid marring the snap-in tabs it'll never reassemble securely. Most video tutorials I've seen show the DIY tech using a screwdriver tip or something similarly hard, marring the plastic tabs in the process. You'll need a tool softer than the plastic. Filing down a wooden popsicle stick or tip of an artist's small wooden handle paint brush should work.

However it should be possible to remove an old cable and thread in a new cable without disassembly. To experiment I disassembled my old broken Revoshift, which confirmed my hunch that it's not designed to be repaired or serviced, only replaced. But I could see it was possible to replace the cable without disassembling the Revoshift. It's a bit tricky to aligned the bits inside to thread it through, but easier than trying to disassemble/reassemble the thing.

After my first experience I bought a complete replacement set of Revoshift 7-speed shifters with cables pre-installed from Nashbar for less than $10, just in case I ever need it.