Is it more work to replace or remove a skylight?
The real answer is:  Don't do anything until you've identified the root cause.  Find the leak.  FLashing and sealant can be replaced a lot more easily than a whole new unit, not to mention the difference in cost and time.
Similarly, if there's a leak where the glass (and frame) separates from the support frame as you open the skylight, address that specifically.

Never start out by attempting the most expensive solution.