Yes! You could have a separate mixer that this noise mixer goes into a channel of- properly treating it like an instrument. Then your guitar would go into another channel. You could replace the second mixer with an interface for example to record both. Having separate channels makes sure you can balance the guitar chain and the noise mixer.
like, brand? any is fine really, i have some from cable matters, some from kirlin, probably some ancient radio shack ones too. get some short 1/4 ones for making connections on the mixer and a longer one to connect to whatever speaker / amp /usb interface you are using.