Yes, extraneous light adds lots of noise. However, since I'm not a great fan of spray paint as my reflector gets hot ...... I use a really simple method that's good for most sources. I add a "slit" in front of the source. No, not a narrow slit like the spectrometer has, but about a 1/4-in slit. This emulates the light source being closer to a "point source" which is what is wanted anyway as the spectrometer's slit is is the only thing providing pseudo-columated light.
Dave