With what your saying about recording software, a 2nd hard drive means you get little lag, and they are not that expensive at the moment so consider getting one.
The software I know you could do this is with XSplit which is usually used for streaming, but you could just set it up and local record on it, or stream on it to a private stream which you can upload from Twitch. Like others have said, its easy enough to sync them. To get the sound and video sync'd make a distinctive sound with action near the start of the recording to allow you to sync them and then cut that bit out. This is what they use those clapper boards for in TV and Film, so they sync the sound to when the bar on top hits the top of the board. You could do that or also record the webcam or camera audio track and just sync them that way also.
Experiment a bit and see how you do!