Gain the summit of Broken Finger Peak
; this is most easily and commonly accomplished by climbing its northeast couloir and northwest ridge
From the summit of Broken Finger Peak, continue southeast along the ridge
to the first obstacle, a steep (near-vertical) downclimb into a prominent notch
. This is the crux; I would rate it as class 3-4, exposed and a bit spicy
, but with pretty good holds the whole way. (It felt like fourth class while downclimbing, but it looks much easier, maybe no more than class 3, when viewed from the bottom).
Once down into the notch, continue along the ridge as it gradually turns east. Following the crest directly here is probably impossible without a rope unless your name's Croft or Moynier; there would be several very impressive gendarmes and vertical notches to negotiate. Fortunately, these can all be bypassed on their right (south) side. None of the climbing is more than class 3 with a bit of attention to route-finding. In general, the closer you stay to the ridge, the better the scrambling and the more solid the rock; lower down, you'd find abundant cruddy loose talus to traverse. Continue along the ridge, traversing numerous ribs and small notches, keeping to the right side where necessary, until you reach the saddle between Broken Finger Peak and Peak 12,760ft+.
From the saddle, you have a couple of options. Following the ridge directly would be most sporting, and appears to be at least class 4-5 with considerable exposure and a number of small, difficult gendarmes to negotiate. Alternatively, the several ups and downs and various obstacles along the ridge here can be bypassed by an easier loose class 2 ramp
on the left (north) side of the ridge. This traverse along the left side eventually leads to easier class 3 rock that leads up to a small notch further along the ridge. (Keeping to the right of the ridge to avoid the gendarmes is difficult here because of cliffs). Climb this short class 3 section up and right back to the ridge, and follow the ridge northeast to join Wheeler Peak's south ridge. The rest of the way up Wheeler's south ridge is an easy but enjoyable scramble over large boulders (class 2).
A number of bailout options are found along the way. (These can obviously also be used to approach the ridge). Along the ridge leading to the Broken Finger-Peak 12,760ft+ saddle, talus slopes appear to lead down to the west and the mines north of Morgan Creek. Several snow couloirs also lead up to this ridge and this saddle from the north, from Tamarack Lakes. Once past Peak 12,760ft+, it's also possible to bail out to the Tamarack Lakes trail via easy slopes to the northwest.
Ice axe and crampons are needed to descend from Wheeler Peak in early season; they may also be needed to safely traverse the ramp on Peak 12,760ft+ at this time of year.