6" deep isn't a "cabinet", unless we're talking for curiosities. It's a bookshelf for softcover books.

Considering a CD is 4.75" deep all by itself, it seems rather improbable to find something that wraps a player around that AND leaves room for cables.

The absolute smallest disc player I've seen are the little USB DVD drives for laptops and such... and even those are 5 5/8" deep, and still need a mini USB cable plugged in.