First things first... is this the printer you refer to?
Teac P55 DVD CD Printer
That printer isn't going to want you to send it (what you think of as) CMYK data (trust me, it isn't ... even if you think it is). What you want to do is feed it sRGB material (technically, using the "Perceptual" rendering intent after you get things setup to a "profiled" configuration).
I did a little TEAC site search and was unable to locate a factory device profile for that machine (as a starting point) so you're going to have to build a custom proofing profile (or, more to the point, find one that is "close enough") and treat the machine as a generic sRGB output device. The nature of the printer is going to make it a little challenging / expensive to characterize the device but here's how I'd recommend you go about it...
What I'm about to describe isn't perfect but it will get you close enough to where you want to be that you can iterate / repeat the process working your way toward an acceptable solution. I don't suppose the machine has any mechanism for linearizing (i.e., calibration) so for the purposes of this thread I'll just assume it will remain "stable" over time. It need not be calibrated per se, but it MUST remain stable / constant in the nature of it's ink deposition (over time) for things to work reliably.
0) Before you start, go read the link below. It's old but will help you understand how to configure Photoshop for proofing in an environment like yours. Keep in mind that you don't (yet) have a known good device profile (you're going to locate a "proxy" for one and use *that*).
1) Open Photoshop and make a 12cm, 400dpi (1890 x 1890 pixel) canvas;
2) Make a layer and paint a 100% black, filled circle (it will look like a black CD, if you're following me);
3) Duplicate that layer (and its content) 9 times;
4) Make each (successive) layer's circle 1cm smaller than the previous one and stack the layers so that each smaller circle lays atop its next largest sibling. If they weren't all black they'd resemble a "cone" when you're done;
5) Save that file (it will become a *template* that you'll want to keep around / re-start things from);
NOTE: The image you are building doesn't look like a rainbow yet but it will.
6) Open a *copy* of the template you made and re-fill each circle with a different color. I would start by picking a Cyan, Magenta, Yellow, a high and low saturation Red, a high and low saturation Blue, and a high and low saturation Green. You're going to want to do this over and over using different colors each time.;
7) Use an output device profile (it should be built into Photoshop) that treats the TEAC as an sRGB device;
8) Print the test file (you should get a nice rainbow colored CD);
9) Use a tool to profile your display (there are lots of pages around the web that will describe how to do this so I won't bother here). You may (or probably should) already have a suitable soft proofing display already set up;
NOTE: Your color critical customers are ALSO going to want to have a proofing display that is properly profiled. If those two things aren't in place you CANNOT reliably tell them what they're output is going to look like without printing a sample for them. NO process you outline for them will help if they don't have a profiled environment.
10) Follow (the intent of) that article (noted above) and select a ICC profile for proofing that best matches the output you got from the TEAC (when viewing it's basis image in Photoshop). You should be able to find something that gets you pretty close.
NOTE: From time to time you may want to make a new sample CD with reference colors taken from customer provided material so you can see how their (various) colors match your proofing profile, etc.
I hope this makes sense. It's kind of hard to describe via this medium.
As for source material from your customers. They should give you sRGB (or properly tagged (i.e., having a correct, embedded ICC profile) RGB material). I would recommend they give you PSD files or (high quality) JPEGs (of the same size as your testing image). TIFFs (and PNGs) are useful too but it won't really matter that much as long as your source material is RGB (or RGB /w Alpha) and properly tagged/described. Some content may best be provided as LAB (stuff with lots of neutrals) but describing that will make this thread too long (so I'll just mention it).
DO NOT do what you thought was correct (i.e., manually convert to some unknown CMYK upstream). Ever...
Whoops: I forgot this link...
http://www.computer-darkroom.com/softproof/softproof_1.htm