It sounds like you have a particular laser, and you don't know what spectrum it's emitting? The best way to answer this question would be to measure your emission with a spectrometer, but if you're asking here, that implies you don't have one.
Let's pretend you got your laser from Coherent. You'll notice that different cavity designs can pick out different emission lines (9.2 $\mu$m, 10.2 $\mu$m, 10.6 $\mu$m, etc), so just knowing that it's a CO$_2$ laser isn't enough to tell you which line(s) are emitted. The spectrum emitted by any one of these models is roughly specified in its datasheet. For example, the GEM-100A 10.6 $\mu$m model is specified to emit from 10.55-10.63 $\mu$m, whereas the 9.6 $\mu$m model is specified to emit from 9.5 to 9.7 $\mu$m.
Where did you get your laser? Can you really not get a datasheet for it? Can you get a spectrometer? Can you build a spectrometer? I've built spectrometers for the visible with gratings and lenses, do you have gratings, lenses, mirrors, and sensors available for ~10 $\mu$m?