Any attempt to customize vim for one-handed use would almost certainly involve remapping a lot of the basic commands -- probably based on the preference and habits of the user in question (for example, which motions do you use most often, et cetera). Since that is highly subjective, I'll mostly gloss over it other than to note it as a likely step in the process.
Because of that, though, one consideration would be specialized hardware that offers more keystroke possibilities to a single handle, perhaps something like a chorded keyboard or even one of those crazy, gaming-oriented "gamerboards." Devices which either re-position keys to put more within easy reach of one hand, or which facilitate a greater number of actual keystrokes through chording, may be able to make up for the efficiency and ergonomics loss of having to use one hand on a traditional keyboard (and thus move it around a lot more to get to all the keys).
Chorded devices are probably more likely, as at some point you're probably still going to enter insert mode and want to type actual text, and I'm not sure how viable that would be on something like that gamerboard.
The mental investment would be high enough that I doubt it would be useful for dealing with the scenario you mentioned (vim'ing while on the phone), but might be more applicable for people with long-term injury or disability that prevents them from using two hands "normally."
Another interesting possibility to consider is that of using two hands, but not necessarily both at the same time. I briefly owned one of these mice, which I found overall to be rather horrid... but its got 12 thumbable buttons on the side that can be shifted to another 12 via a ring-finger button, for a total of 24 distinct inputs. It made me think there might be a scenario where you could find some useful vim commands to map to those buttons, ones you found yourself using near when you also found yourself using the mouse for outside tasks, for example.