What would be the point? That mask is the proverbial screen door on a submarine in that scenario.
So your answer is no. Would that also mean that the health care workers "need" for masks because they were working on CoVid-19 wards was purely psychological?
I'm a big proponent of "concealed is concealed" and "don't ask, don't tell" with respect to carry of my firearm, and my decision-making process has nothing to do with what makes anyone else feel safe or unsafe. That is, granted, different from the mask scenario. But just as someone who approaches and accosts a firearm carrier because they "feel unsafe" disproves their assertion of feeling unsafe through their bold act of approaching and accosting the firearm carrier, someone who approaches and accosts a mask non-wearer because they "feel unsafe" belies their lack of truly feeling unsafe, by their willingness to enter into close proximity to the mask non-wearer, thereby exposing himself to the very risk he claims to want to avoid.
Your assumption is that the person approaching is concerned about themselves.
Government has no authority to compel healthy people to wear masks. Government has some authority to compel verified sick people to act in certain ways (such as enforced quarantine), but that authority does not extend to compelling those who are healthy.
I'll leave that to the experts to determine. Government has a lot of authority I don't even know about.