Sure you can! Either siphon it to the new keg, or get "fancy" and use a piece of beerline with disconnects and go from the "out" side of the leaky keg into the "out" side of the new keg. You'd need a black disconnect on each end. If you go from out to out, they'd be no splashing- it would go in through the long dip tube into the new keg. Then, push it with co2.
Me, I'd probably just siphon it.