I think the site is down now, but the Wayback Machine should be able to find the Kiev Survival Site, which has well photographed and explained documentation going as far as shutter cleaning and lubrication. Lots of little parts and they have to go back just so (as one might expect of a slightly updated pre-War Contax design), but few if any "jack in the box" springs, and the whole thing is within reach of mortals (provided you don't have too much kitty assistance).
Of course, there's also the option to get an actual Contax, which shops will work on. Last I looked, you could get a pre-War Contax II or III for around $200 on eBay, with a little patience, and then another $125 (and up) for the CLA it will probably need after 80+ years...