Without professional training in ice-axe/crampon use...and practice...you might rethink your plans for Mt. Whitney...and Shasta! Yes, there probably still be snow on Mt. Whitney and maybe on the approach. There have been several late season snow storms which have added to the snow-pack depths.
Bob Pickering (post above) offered good advice on the topic.
One cautionary note:
There may be shops that will rent ice-axes and crampons, to anyone with the money and zero experience. It would be far better and safer for you to take the training, buy your own equipment, and practice regularly. This is not something you can learn very much from a Youtube video. It takes hands-on training and practice.
When I was with Inyo SAR, we had to retrain in self-arrest annually before we were certified to join snow-country rescue missions, even though we were all very experienced. Does that tell you something? I hope so.
Last edited by Bob West; 04/13/20 10:28 AM.