Are you sure it's the cement that's causing the haze? In my experience, bad lens cement usually looks more like chipped glass around the edges or bubbling. Haze is usually something different. Haze, in my experience, is usually either a result of fungus or some kind of chemical, like oil, vaporizing on the lens elements. Besides, those Contax lenses aren't that old. I wouldn't think a lens that new would have lens cement issues unless there was a manufacturers defect. I've got several 100+ year old lenses with good cement.
I've come across several lenses with what I'd call haze, and usually, I just remove the elements and clean off the haze with a microfiber cloth and reassemble the lens. It's easy to do with a spanning wrench. The trick is having a system so when you put it all back together, you don't accidently flip a lens element around. It also helps to take lots of digital photos as you go to help you if you get lost along the way, and mark the position of any lens element that may be adjusted (making finding it's exact location problematic without a system. The hardest part is coming up with a clean area so you don't get a bunch of dust inside your freshly cleaned lens when you reassemble it all.
So no, I've never sent a lens out for a cleaning. Unless it's a very expensive lens, it would probably cost more than buying another used one in good condition. And unless we're talking about a zoom lens, I probably wouldn't hesitate to open it up myself. Manual focus lenses usually aren't too complicated so long as you're not digging around the aperture, leaf shutters, or helicoil.