Gunship,
Probably a 17 at this height. They all look the same don't they.
2 guys were rescued higher than this by a 350B2 a few years back. Fuel was staged on the way up and it definitely would not hover. They were lucky was hard snow and it basically just fell off the mountain each time. 2 turns. Oxygen definitely required! The rescue was at about 22,500 AMSL which is outside the service ceiling for this aircraft let alone landing or hovering. Who knows what the DA was. Leave the Flight Manual at home - too heavy.
I have seen the footage on the BEEB and it seems he clipped a hut in a turn. Tough call as I doubt there is much published data available for this operation.
Anything you do up there on Everest is risky.