Sorry - slightly confused - are you saying you want to travel home 'en femme' with the splosh substances inside (but you say you are shy about CD?) or will you just be wearing the lingerie under your 'drab' clothes? Either way, it will depend on how you intend to travel. If you're travelling by public transport, you can't use anything that will leak out on to the seats as that would be unfair to anyone who sits down after you (and the bus/train company cleaners)! (You can put bin bags on the car seat if you're driving or not worry about it at all if it's only a short walk!)
For the latter, how about creme eggs (if you can get them at this time of year?), which I gather are a slow (and somewhat random) melt. So long as the tights are of heavy enough denier, they probably won't leak through but should all be retained between your legs as you walk, which should feel nice.

Not quite sure how you plan to dress in the lingerie shop, however! You're a better CD than I am Gunga Din!