I have a high voltage (750V) high value electrolytic cap about as big as my forearm. It has been in my storage box for about 20 years. In general, do electrolytics degrade under normal storage conditions ie room temperature over such a time? Not quite sure what type it is, but probably a standard Aluminium foil, not solid state. If they do degrade, what characteristics degrade?
The main thing that degrades is the aluminum oxide dielectric layer on the surface of the aluminum foil. It's also possible that electrolyte (or at least its more volatile components) has leaked through the seals.
You can try to re-form the oxide using the procedure that @Transistor has outlined: Use a variable DC voltage source to bring up the voltage on the capacitor gradually over the course of several hours. Monitor the leakage current carefully, and if it starts to rise out of proportion to the voltage, hold the voltage there and see if it goes back down.
The only thing that will make it "pop" is excessive power dissipation, so keep track of the power, and if it rises above a watt or two, you're probably out of luck.
If you get to full rated voltage successfully, you still need to measure the actual capacitance to verify that you haven't lost electrolyte. Be sure to discharge the high voltage first!