I carry a small bag with valuables. It is small enough that it doesn't bother me but big enough to carry a few things. I have the Overland Equipment Placer, and it has a zipper pocket on one of the flaps where I carry money, KTTW cards, id, etc. I carry my cell phone and a small camera in it, too. I bought it for Disney, but I have used it on day outings and other vacations. Because it is small and comfortable, I can wear it across my body and keep it on me at all times (rides, even at restaurants).
We used a larger bag for non-valuables (kid-related supplies) and hung that on the stroller.
Or you could just have DH keep the KTTW cards in his wallet.