Welcome to the site sleepypig
That's an interesting question that hasn't come up before..
It's not currently possible, at least not in an easy way. You could try using a Windows Object Capture and selecting the interior area, but that's definitely more work than just performing an active-window capture.
One thing i could do if this is a feature that more people want, is add some menu function to automatically trim off some amount from top,bottom,left,right, either at the time of capture or via a menu action -- that would let people pretty easily remove titlebars and/or borders...