My advice would be to get a small USB PA mixer (my current favorite is the Yamaha AG06). You hook up your DDJ-SB to one channel, you can hook up 1-2 mics if you need them and you can set your FL output to the Yamaha. Now everything you play will come out of the speakers that you also attach to the Yamaha. You will have individual control over all input sources so you can make them all sit nice in the mix.
You can then send the master output from the Yamaha through USB back to (for example) Audacity to record that signal (I think the mixer even comes with an LE version of Cubase, but not 100% sure). And presto!
Having a small PA mixer handy is ALWAYS a good idea in our humble opinion. Prices are very decent these days, the AG06 comes in at about 150 euro or so. Hardly a bank breaker.