I would also like to ask you whether there is any material that is flexible enough to form in your palm under small pressure, but tense when formed under strong pressure
Look into:
- non-Newtonian fluids, D3O material has been used in product design
- plastic mechanophores, most interesting for smartphone cases. Research is being done currently, I haven’t seen a commercial mechanophore plastic yet.
- nanomaterials that are activated electrically
The friction of your handle to the skin is also important - the handle will need to curl up smoothly rather than the edges sticking into the skin so I recommend using a plastic like 3mm polypropylene with live hinges or overmolded silicone for the hinges.
By the way, you can also take pictures while using the smartphone horizontally and clicking the volume ‘up’ button 
People will generally don’t use this much because they have a less steady hand on the smartphone. So if you design proper indentations with grip areas in the side of the cover you may also have a marketable solution.