There is no need for an ice axe. Wear gaiters to avoid getting scree in the boots. Everything on this mountain tumbles, slips, shifts, slithers and falls. In combination with nearly 5000 ft of gain within very few miles, it gets to be a strenous day.
The description of the route in Secor is dead-on and so are the PCS and SPS trip reports.
Here is an attempt at describing the route:
Drive to the left end of Convict Lake as far as the road will take you and park at the furthest parking lot. You are 2/3rd of the way of the length of the lake. Hike through brush to the first ridge line on the left of the lot. You will meet an old jeep road, follow it till it ends in a short distance at a stream. Follow this stream up, keeping it to your right as it comes down a beautiful verdant valley. The stream seems to originate from a small tarn. There is another tarn further up which looks like it is turning into a meadow and then there is a much larger tarn further up.
By following the stream, you are going behind (south) the front peak (10800+) that blocks the view of Morrison. Turn right (west) at the small tarn towards a cirque like valley that is on the lower reaches of Mt Morrison. A steep trail switchbacks through this valley till it tops out below Morrison's east face. One of the many options to reach the summit is to go straight up this face over class-2 and sometimes easy class-3 stuff. This is the worst part of the climb. The summit has outstanding views of Red Slate, the Minarets, Ritter, Banner, the Inyos and the black, foreboding face of that equally loose and unstable peak, Red and White.
Thanks to the many listeners on the PCS/SPS email broadcast who offered useful tips and suggestions when I had asked about conditions at Convict Lake and on Mt Morrison.