LEO is not accessible by space elevator at all. If you got off at ISS height you would just fall down.
Good for basejumping though. And no you wouldn't even need heatshield, just rugged EVA suite.
As you're going up the space elevator, you would also be picking up horizontal velocity as you ascend. At ISS altitudes there would be enough atmospheric particles to slow you down once you got off, but it would take a while; probably on the order of years. Base jumping would not be a good idea.