Hi Jeff,
I would think super caps would be rated differently because some of them are so low in voltage rating already, but i dont use these things on a regular basis either.
I see your problem with going to a bigger size battery might be such that they wont fit in the original battery compartment. This is just an idea, but in the past when i was faced with this problem i just extended the battery compartment artificially to make it large enough to hold the new batteries. In fact, even an external battery holder would work. That is of course if your device and it's normal use can tolerate the somewhat larger size of the entire package that results. So applications can not and some have no problem, especially those that dont really have to be portable. For example, something that is mounted on the car dashboard may not matter if it is a little bigger, but if you have to carry it in your pocket then it starts to become a little cumbersome if it gets too much bigger.
Just an idea though, it's always your call.