In this wacky scenario, one must take into account the physiology of the human body at altitude. A decompressed airliner at 35000 feet would affect ALL on board, crew and passengers unless the 777 has a cockpit that is somehow sealed from the rest of the aircraft for which I am not aware. Also, the oxygen system on the flight deck, as well as the walkaround systems used by the cabin attendants, is much much more sophisticated than those plastic drop downs in the passenger cabin. Oxygen would be required once cabin pressure gets above about 15k. In aerospace physiology, a term used is “time of useful consciousness” or TUC....TUC at 35k without O2 is between 15 to 30 seconds, depending on the individual...even less in some, particularly after a rapid decompression. TUC above 40k is maybe 5 to 10 seconds. Above 40k, unpressurized cockpit, 100% oxygen must be administered under pressure through the mask, for the human body to remain functional. The higher you get above 40k unpressurized, the more the pressure is required in the mask, and you must have to forcefully exhale against that mask pressure to get the 02 into the blood in the lungs. These physiological facts are why most airline flight ceilings are in the mid 30s for almost all airline activity. Business aircraft are frequently above 40k, think Mr. Payne Stewart’s ill fated flight. IIRC, above 40k, one crewmember MUST be on oxygen at all times, I.E. MASK ON...in the Stewart incident, not sure those regs were being followed. Also, unless the MA crew had not been breathing 100% O2 since at least takeoff, aka prebreathing in aeromedical physiology, to rid the body of as much nitrogen as possible, a decompression, weather intentional or otherwise to those flight levels, aviator decompression sickness, or the “bends”, comes into play. Particularly if the flight were to continue at those altitudes unpressurized. That is one of the most primary physiological concerns following a decompression at those flight levels...and the need to get to a lower altitude without delay, not just for oxygen supply and TUC concerns, but to also get barometric pressure back on the human body, to keep nitrogen in solution, and not let N2 come out of solution and into bubble form...aka bends. Above 50k, a decompression would cause the human blood to basically “boil” from the lack of barometric pressure on the body as N2 comes out of solution. Thus the reasoning for pressure suits used in all military flights above 50k...U2, SR 71, shuttle etc... Aircraft decompression is usually one of three types. Insidious, a slow leak for instance, rapid decompression, a window or door “popping out”, and explosive decompression, usually caused by total destruction...think shuttle Columbia here, or possibly that Hawaiian airliner that survived the cabin top basically tearing away in flight.. Explosive means the air escaping the vessel, (aircraft) is faster than the speed of sound.
There is no "walkaround system" used by cabin attendants. At least there was not when I was flying and I was trained on the 777. The rule is "if you see the masks drop, immediately sweep the nearest one to your face, sit down (or get down on the floor) and hold on, because the plane is about to dive." That is why there is an extra mask at every seat row - for cabin crew and/or laps traveling without a seat.
I was trained that you immediately put the mask on because within seconds you will not be able to do so - you lose your coordination and wouldn't physically be able to hold a mask or put it on, much less help anyone else.
You are right that there are 3 types of decompression: slow/gradual; rapid; and explosive, but an explosive decompression does not mean total destruction. UA 811 was an explosive decompression (cargo door ripped loose) that happened at around 22,000 feet; Aloha 243 was also explosive. One of the flight attendants on 811 was hanging on to the stairwell railing for dear life, waving like a flag in the wind. If the event had happened at a higher altitude, she would have been sucked out of the cabin, as she would not have been able to hold on long enough. Explosive decompression is very obvious. Rapid and slow decompression are very dangerous in that you might not realize what is happening (you are still able to breathe in and out) and can be under the effects of hypoxia before you can react.
I had a coworker who was involved in a rapid decompression where there was no explosive event; the masks just suddenly dropped and for the first few seconds, the cabin crew did not react because there was no apparent reason for the masks to have deployed (no bang, no fog, nothing obvious). It wasn't until the rapid descent began that they realized they were in trouble. My friend had damage to her sinus cavity - the lining of her sinus tore loose and caused her horrible problems later on. But immediately during and after the event, she had not felt anything, possibly because she was already under the effects of hypoxia.