I've been looking into this (near) exact scenario for a friend, there appears to be a lot of info on this topic. The card can run on a low profile system with a 250w psu, but without testing this I am hesitant to make a recommendation. The "min 400w" they slap on these cards is usually because they test them on a high end system with a lot of current being drawn to other components. Thus by including the higher power rating they can cover themselves if anything does go wrong.
Sorry for necro, you've probably found an answer by now anyway