Hmmm. First of all, I guess you are thinking in terms of September. If there is any snow at all then, it is likely to be very new snow, and that is not so bad as old snow and ice.
I went up and down Whitney in June. There had been a snow storm just two or three weeks prior, and I had seen the new photos of snow covering the entire Switchback slope. As a result, when I drove over there, I took an ice axe and Yaktrax. Then when I talked to rational people at the visitor center, I realized that they were not needed. There was a path about eight or nine inches wide beaten into the snow. Of course, that is all gone now, and September might have something new. Remember, though, that you are not the Lone Ranger out there, and many hikers will be using the same trail ahead of you.
You could probably wind some parachute cord around your boots in a crisscross fashion. That is done in Japan using ladies nylons twisted into a rope. You want to get the rope about a quarter inch thick so that it mashes down under your weight, but it gives you a little traction.
Start with a long piece of cord and find the middle. Tie a loop there that will fit around the toe of your boot, but it won't slip all the way back to the laces. With that loop around the toe, do crisscrosses as you wind it back onto and under the boot. Then tie it off with the regular laces. That won't be perfect unless you keep it tightly on.
If you have trekking poles, it won't be so bad.
On the other hand, if you get up there and get stuck and die, then we will divvy up your gear.