High voltage capacitor, in a low voltage system?

No, having a higher rated cap will not somehow store up more voltage than is available in the circuit. You actually want a cap with a slightly higher voltage rating than the highest voltage you expect to put across it. In fact, if you put more voltage on a cap than it is rated for, it is apt to catastrophically fail, i.e., pop or explode.

While not a perfect analogy, think of the voltage on the capacitor similar to the liter capacity of a tank. It will hold "35 V" but you needn't fill it completely. But like @JustJeff said, you'd be wise to ensure the container can hold more than necessary to prevent spills (and in an electrolytic capacitor's case, the electrolyte can expand and quite literally "spill" out).

Note that a better analogy to capacity would be the farad unit, since that's a measure of a capacitor's charge capacity, so don't get that confused with voltage, which is the potential to do work.

If a high-voltage electrolytic is used at low-voltage, the actual capacitance might be a lot lower than the stated value.