RB, even after the driest of winters, May 25 is an extremely early time to use the switchbacks. Here's a link:
When will Mt Whitney switchbacks open?

I think your chances of using the switchbacks are 50-50 or lower. You will definitely have significant snow above Trail Camp. You should try again on May 1 to see if you can get something later in the summer.

Beginners using the chute is not optimum. If you had someone with experience to show you the techniques, including ice axe self-arrest, that would be best.