OK. If the file has no profile, that's when the working space takes effect. The problem with that is of course that it only applies to your machine. On another system it may look completely different.
But at least it tells you which profile to assign: the one you had set as working RGB when you created the file. That's the color space it was created in. If I recall correctly that would be sRGB in the general purpose presets.
Now, CMYK is a completely different animal. I would recommend that you do not go there. Keep it RGB.
First of all, CMYK is strictly for commercial offset printing. Inkjet printers expect RGB data (they do their own conversion to the actual inks used in that particular printer. This is done internally in the printer driver). So for standard inkjet printing, it needs to be RGB.
Even assuming that this will go to commercial offset printing, there is no standard generic CMYK. You need to know which CMYK profile is appropriate, and if you're selling this you have no way of knowing.
A CMYK profile is a characterization of a specific offset print process - a press calibrated to a certain standard, using certain inks on certain paper stock. These standards vary widely. You need to know in advance. So if you convert to one CMYK profile, you can actually ruin the file for the buyer if it's intended for a different process.
The de facto standard for web is sRGB. This has the highest likelihood of being correctly represented in the highest number of possible scenarios.
For inkjet printing, Adobe RGB is universally preferred and will be accepted everywhere. It translates well to most inkjet print profiles. But note that if your file is already sRGB, there is no real point in converting. sRGB is smaller than Adobe RGB, and converting won't change that. If it is sRGB now, I would just leave it as sRGB.
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