Now I know the button you mean.. its the release to open the armrest.
I've prowled through everything I have and cannot find a work procedure to specifically go after that part. Sorry. You'll just have to dive in. :-) Maybe somebody else here knows.
To the best of my knowledge, there is no factory service CD for the W140s... I've heard rumor (on this board) that MB is going to release one in the future, but cannot confirm.
In the meantime, Alldata is a good compromise... its about 25 bucks a year. Lots there on console disassembly, but not the specific part you want (unless I simply cannot find it).
That button on my car was also soiled and worn... I bought a leather dye kit and redid it without removal... looks like new. You might try that unless you have a craving to do the woodwork...