This is an amazing route that I liken to the Knife Edge on Katahdin. Not ever having been to this area in New Zealand before, I just wanted to see if this ridge went and didn't cliff out. Well, it doesn't cliff out (although you really think it is going to a few times before you look over that gendarme and see that there is a way down) and this was pure joy for me. Probably a half mile (or about a little less than a kilometer) of Class 3 ridge scrambling with one move of Class 4 at the end. The exposure is never really that bad, just fun. Views are amazing along the way and really, if you wanted to, you could probably bail off between gendarmes at several points if you found it too loose or unenjoyable. I would highly recommend this loop hike to include Avalanche Peak, Lyell Peak and Mount Bealey, I don't think you'll be disappointed.
Crux Class 3-4 Chimney
Some exposure of you fell and rolled off right but it is not that bad and can be avoided in the grassy slopes to the east. After that, cruise up to the cairned summit.
To descend, I would suggest the Bealey Track which follows the cliffedge from the summit down east. There is a trail with high steps and Class 3 in areas. Once down to the saddle and up to Point 1760, directly east of the summit, follow the ridgeline as it curves then northeast to the treeline. Pick up the cairns and follow to the trees and the signed trail to the Bealey Track Trailhead on the south side of Arthur's Pass (several kilometers south of Scott's Track where you started most likely so a shuttle or pickup should be arranged unless you want to walk the road into town).
To do this route from the Bealey Track, just reverse everything I just typed above and follow the ridge north to Avalanche Peak where you can take either Scott's Track or the Avalanche Peak Track back down.
Note-One hiker indicated that from around Point 1760 you could ski the scree down to Rough Creek and follow it out to the Bealey Track Trailhead. I have no proof of this but did see it mentioned in one other book. If you try this, I would suggest being careful if water levels are high.