While I am a big fan of hydraulics having played with it most of my life on the farm I don't quite see how this will make it easy. Your tower will have to be safety pinned on the side opposite from the hinge to be safe as a hydraulic piston isn't safe to use as a holding support. You would need to climb half way up to pull pins and put them back.
I think that hinging at ground level would actually be a better way but would require more engineering and heavier duty construction. If by car hoist you mean a car jack for changing tires then no I don't think that will work. Since you say push a button I am thinking of one of the units like operate a lift gate on a truck and yes that might work with the right valving, cylinder and holding tank.
The hinged with counterbalance sure looks nice. If you want to push a button a good 12 volt winch should work well with it and is probably cheaper than hydraulics plus being more portable. I know I keep looking for a good enough reason to buy one that will convince the wife.
How do you plan on building the tower as that would help give more of an idea on how to do this?
Finis