I share your pain, I have cramped facilities here as well.
As to size and voltage, you will typically find that (example) a modern 4700uF 35V capacitor will be about the same physical size as a 1980s 4700uF 12V or 16V capacitor. The main penalty for using a higher voltage capacitor than necessary is cost - the higher the voltage, the more a capacitor of a given value costs.
Despite that, I usually replace old capacitors with ones of similar size (therefore higher voltage rated) to keep the equipment looking 'right', and also, if the capacitor will be working in a warm environment then the more electrolyte it starts off with inside it, the better, since it will then take longer to dry out.
Maybe this is being unnecessarily far sighted. Anything I re-cap now is very likely to out-live me by a long way before it needs to be re-capped again.