That changes the game a bit. If the logic is that he is committing a violent felony even with a known fake gun and is still a risk to folks, then shooting him is quite acceptable. He might have a knife as I posed and could have pulled it out.
However, I was commenting on shooting him has a measure of social house cleaning because you knew that he was not a risk with the fake gun but you get a legal free shot.
That is a personal philosophy question of eliminating a nonrisk for whatever reason. I certainly agree with eliminating a violent risk.
I might conclude that the act of the robbery itself with the threat of force itself is a justification to shoot. Not shooting is based on tactical situations as you decide what is the best outcome path is reasonable also.
I still don't want to wrestle with the dude as most bank robbers tend to leave. It's a risk call. Fake gun man probably wants the money and to go. Will Fake gun man risk a hostage, probably low odds on that but it could happen. However, I think Fake Gun Man flees and that's a little risk of harm. YMMV.