To me, it's not such an issue of someone else finding it; it's a legit prescription as far as they're concerned, it's not like you have a cellophane baggie of pills. I think it's more of an issue, do you have the willpower to resist taking them later and ending up where you were before?
I believe refills for a schedule III expire in 6 months. So, you've got some time to decide, but you never know when there's going to be some extremely painful day...then again, one little relapse tends to mature into a full-fledged habit. Please be careful.
I personally would refill it just to have, but that's a decision you have to make based on your likelihood to take it when you might want a little extra than ultram and tylenol can give.