Yes, it's possible. Whether or not it's advisable is up to you. I've done it, but I'm crazy like that.
As others have said, if it's still under warranty, you'll void the warranty. As far as I know, there are no actual guides for doing this, but it's fairly straightforward.
Disclaimer: None of this should be attempted unless you're reasonably certain you'll succeed. It does require basic electronics and soldering skills.
Depending on which setup you have, the wiring is either really simple or complex. With a stunt setup, it's basically just two wires, a switch and an LED. All you have to do with a stunt is take the switch out, either desolder or snip the wires (best to take the batteries out first) and then snip the negative (black) wire going to the battery pack. After that, the battery pack will come out one end, the LED out the other end. Put that in the other saber, solder the switch wires back, and the negative wire back together and you're good to go.
Sound is much more complex. Obsidian wiring diagrams can be found here:
http://www.saberforum.com/index.php?topic=6717.0Don't worry, it hasn't changed for the V3 and V4. V3 and V4 setups usually have a buck puck, which is attached to the battery pack and board right under the front of the board, and is wrapped in electrical tape. There should be 4 or 5 wires going down into the hilt from this. Two are white and blue, those are your battery positive and negative wires. Two more should be the same color (US usually uses gray) and are your switch wires. If you have flash on clash, that's when you'll have a fifth wire. Snip all of these. Take the whole battery/board/speaker pack out, take your switch out and your LED, transfer that all to the other hilt and resolder the wires.
Don't ask me about Emerald or Diamond setups. I have no experience with these. Also, I'd assume Obsidian Lite is basically the same as V3/4, but the wire colors might be slightly different as it won't have a buck puck.