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.
As a former USAF Physiological training instructor, in a training field where we trained pilots, flight nurses, aircrew members,VIPS, guests, etc., the medical affects of altitude on the human body, I probably went through close to a thousand rapid decompressions in hypobaric chambers. We called them RD's....and normally in my days, rd chamber flights simulated an actual decompression from 8k to about 22-25k.. Been away a long time, but I would suppose the training profiles are much the same.......yep. you dont have to clear your ears on the way up, but you do on the way down....sinuses are another matter...I have seen some painful sinus problems with both trainers and trainees.
and in regard to the supplemental oxygen systems aboard a 777, I am totally un-informed, but in my passenger flight history aboard commercial airliners, I have seen "walkaround" bottles stowed in some aircraft...btw, we used them all the time out of Kadena back in the day...while pushin leaflets out the backend of a HerkyBird over North Nam, unpressurized with the ramp down at fl250 give or take a few...usually around 0200 or so local....with an ECM bud about 10k overhead, paintin a hundred radar targets on NV scopes..