I always wear my tri shorts when doing a du, but since you don't have any with that little padding- try running in your shorts that you have and see how they feel. You may be fine- you may chafe. I guess the only way to tell would be to test it out. If you're really not concerned about placing- then maybe you could wear the running tights- then pull your shorts on over them for the bike ride and then whip them off in T2 and just wear the tights for the last run. No chafing from the chamois then (and who cares what it looks like- cuz nobody's really looking anyway).
Let us know what you decide to go with.

Good luck with your race this weekend- we want a race report you know...