Don't forget Bandicam! It works just as well as fraps, and the free trial lets you record for 10 minutes, rather than 30 seconds. You can make 10 minute videos, cover up the watermark whilst editing, and pretend you have fraps! (Not that I'd do that... I have the full version of Bandicam. That was just hypothetical...)
I'd suggest turning Minecraft's brightness to full. If it's on "moody", nobody will be able to see anything when you're down in a cave!