Replacing the factory CD player
 

Hello all, This weekend i was finally able to afford the little convertible that i have been wanting. Not new of course but i am sure with some money and effort i can really make this car everything i want it to be.
First let me apologize for the long post, i just want to make sure i describe my problem in detail.

It is a 2003 Mazda Miata Shinsen Version
The problem i have is that after getting it home and driving around i have found that the CD player skips really bad. And it annoys me to no end.
But i am having a problem finding a solid answer about how i can replace just the CD player with an aftermarket head unit.

My system looks like this (or at least this is the closest picture i found):
http://img140.imageshack.us/img140/412/1m31sm.jpg
They list this as the BOSE system, but mine does not have BOSE written anywhere on it.

It looks more like this one, with the addition of the tape deck below the radio and CD player:
http://img696.imageshack.us/img696/2592/4162sm.jpg

So i am assuming that i have the non-Bose system, and that the initial owner had them add the tape deck (Factory not aftermarket).
Can just the CD player be replaced?

Online i have gone to audio sites such as Crutchfield who say that the Kenwood KDC-138 will fit my model car. But i can not be 100% sure because i do not know how exactly to describe which type of stereo unit the car has:
Single-DIN NB Audio System (1M32, 4M32)
Single-DIN NB Bose Audio System (1M31, 1M37)
Double-DIN NB Audio System (4162)
Double-DIN NB Bose Audio System (4H60)

Any help would be greatly appreciated.
Steimy