How common is use of word "PhDs" to describe PhD holders in formal documents?
Extremely common, in both general usage and in my exposure to professors/academics. Unless you have some reason to believe there would be objections to it, I think you're anticipating a problem where none exists.

(On the other hand, "saving characters" is an awful reason for doing anything, especially these days when memory is cheap and printing is easy. If you use this form, use it simply because that's how people talk.)