If you have 10 mics plugged in at all times, I can see that'd be a bit of a mess. However, if you're using good-quality XLR cables and using proper XLR connections (i.e., no XLR-to-1/4" connectors), there's no reason you should be getting a lot of noise unless the cables are very long indeed.
I've never heard that parellel cables add noise simply by virtue of them being parallel, (although I'm not as electrically inclined as I could be).
Are the mics all plugged into your audio interface, or are they plugged into a mixing board first? Have you eliminated the board as a source of noise? If the board is plugged into your computer (I would hope it is!), what cables are you using? TTry testing them for noise as well.