The objective of an emergency descent is to bring the aircraft down to 10 000 ft as fast as possible.
Why? At 41000 ft you have some 10-15 seconds before you pass out. Then the clock is ticking towards brain damage.
Start the emergency descent while you declare and squawk emergency. Any advice after this point from ATC is very welcomed, but I will not start a debate with ATC before I start to go down. There is no time for that.