If thats your concern, I wouldnt be worrying about the 10 seconds your protein shake is in there...I would be WAY more concerned with the days/ weeks...Coke, Milk, bottled water, etc. that you consume on a daily basis...is sitting in the container.
I think it depends on the plastic. I would think the plastic used for those shaker cups is a cheaper grade and probably more dangerous.
10 seconds , nah, hardcore lifters bring their drinks to the gym and sip them throughout the workout , so it could be in there from anywere from a half hour to 2 hours. I think Milos recommended to do this, sip the protein during the workout. or drink some before and some after the workout.