Unbalanced connections are not necessarily "bad", as long as you realize the limitations of them.
I won't bore you with the nitty gritty electronics behind balanced versus unbalanced. Balanced connections have the advantage of being much more resistant to external noise getting into the cable. They also are able to be used over considerable distances (up to 2000') before you start getting signal degregation.
Unbalanced cables are just fine for short distances.
Now, what do you do? Personally, I would forget about the XLR cables you have and just get some good RCA-RCA cables in a length that works (I like to keep 'em under 10', and shorter if possible).
If you are hell bent to use your XLR cables, then you need more than just adapters...you need matching transformers. A matching transformer will convert the unbalanced signal from your CD player to a balanced signal, which then can be run as far as you like without picking up noise or loosing signal quality. But, that's going to run you at least $50 for a pair.
Sure, you can get adapters cheaper. But all an adapter will do is let you go from one kind of connector to the other. You will still have an unbalanced signal, which means you could be picking up noise (especially if you have a computer nearby).
Just go with the RCA to RCA cables. That's your least expensive (and best) solution in my book.
Good luck.
Greetings from Austin, TX
Ken