I've never changed the battery on my Kronos X, which I got around 13 years ago. When the Kronos and Nautilus batteries go, I plan on opening it up, myself. I've changed batteries on the OASYS a couple of times, but that only requires 2 screws to lift up the "hood." Kronos and Nautilus have a bunch of screws on the bottom. You put them on a soft cloth, upside down (don't let the screen rub against anything), and take the bottom off, being very careful with the keys assembly.
I haven't opened my Nautilus, but it should be very similar to the Kronos. I took all the screws off and removed only the bottom panel.
Changing Kronos battery:
https://www.youtube.com/watch?v=ElQHaeQGllM
Nautilus insides:
https://www.youtube.com/shorts/bzMxm1QmHSg
Resetting the clock after battery change:
https://www.youtube.com/watch?v=DRsDsUYfqr4
Note: I believe that opening it up yourself will void the Korg warranty.