This is probably the most important point regarding everything that happens post landing in Seattle; Cooper already feels like it's taken longer than it should have to get on the ground again and then it takes forever to get the fuel on board. Each new stage of the hijacking (getting the money, chutes, etc.) has to be fast tracked and trying to use his actions at this point to identify who he was or what level of experience he had is going to be somewhat flawed.
His ability to keep moving under those circumstances is good evidence that he a) felt comfortable when it came to parachuting and b) had his wits about him to not freak out and keep moving forward with the plan, adapting to try and keep to a basic schedule as best he could.
Cooper knew parachutes enough to deal with what he got.