I am quite surprised that an airline would allow their crew to use slippers while operating a flight.
You first need to check the airlines safety policy in regards applicable footwear.
If there is no such policy then the next best thing is to check with the local safety office of DOSH (Department of Occupational Safety and Health) for their specifications.
If none then I suppose you may want to refer this matter to your in house union for them to look into it.
You may just start your upper management personal jumping as this would definately involve some cost and being management, they would most likely to side step the issue.
If you think that this is such a safety hazard, do not back down. Go for it!!!