To bend bounds form the natural 90 degrees require an energy source to do the work of bending. That is why I think the 105 degrees between the two protons is best thought of a due to the electrostatic repulsion between them - that can do the work of bending 90 to 105 degrees.Contrary to popular belief and countless low-lever chemistry textbooks, the non-bonding electrons in water don't really have much to do with the bent shape. Based on the bonding within the molecule, the protons would ideally be 90 degrees from each other. But this would cause the protons to bump up against each others van der Waals radius, so they bend their bond angle slightly to be farther apart from each other.
Although one can define a radius for the proton, I have no idea what you mean by "bump up against each others van der Waals radius." How would that radius be defined? Do you think the 105 degrees is dynamic - increasing when they "bump"?