Bear in mind that a skydiver falling before opening his parachute is encountering air resistance, which means he's not really in free fall (in the relativity sense). But let's imagine a hypothetical skydiver falling through empty space. In this case, there is no difference at all between the person in the free-falling shuttle and the skydiver in free fall outside the shuttle.
At first, I wasn't entirely clear about what you meant by
but you can't 'push' yourself up like you can while in a free-falling reference frame (like the shuttle)
but based on what has come up in the comments, I think this explanation would help: when you throw a ball downwards as you're falling, you move up relative to how you would have been moving otherwise. This holds true whether you're in an enclosed environment or not.
The reason it may seem different is that, if you're in a shuttle, when you throw the ball, your motion changes, but the shuttle's doesn't. The shuttle gives you a convenient reference for how your motion would continue if you hadn't thrown the ball. So you now observe a relative motion between yourself and the shuttle, whereas before the throw there was none, and it's obvious that your motion has changed.
It's worth noting that it's not necessary for the environment to be enclosed in order for this to work. If, instead of a shuttle, you had a friend skydiving next to you, and you threw a ball down, you would notice yourself moving up relative to your friend.
On the other hand, if you don't have a shuttle or a friend or anything else falling along with you, there's no other object to serve as a reference for how your motion would have continued. So when you throw the ball down, as a human, it's difficult to notice that your motion has changed. There's no switch from "not moving with respect to X" to "moving with respect to X." Instead, the only convenient object which you have to measure your motion against is the Earth, and you merely change from "falling toward Earth" to "falling slightly slower toward Earth."
Bear in mind that the actual change in your motion is the same as in the other cases, where you had a friend or a shuttle or something falling with you. If you had measured your motion relative to the Earth, instead of relative to the shuttle or friend, then you would see the same effect: you would change from "falling toward Earth" to "falling slightly slower toward Earth." It's just that the limitations of human senses make it hard to detect the difference between those two motions; it's much easier to detect when you start moving relative to something you were previously at rest with respect to.