Frank would not have killed the manager
The Punisher's code, brutal though it may be, has always focused on killing only the guilty. While the manager may have committed some crime, certainly Frank did not know anything about him. Most likely, had the manager attempted to investigate further, or had Daredevil screamed or otherwise drawn the manager's attention, Frank would have knocked both him and Daredevil out and left. Frank was always willing to miss out on a kill in order to avoid killing innocents, as illustrated by his refusing to shoot Grotto while there was a risk that someone else could die.
Frank has certainly killed nonviolent criminals
The most obvious case is Clint, the man who sold the Punisher a gun and a police radio. Recall that Frank beat Clint to death after Clint offered to sell him child pornography. While the production of child pornography may well be violent, selling it, reprehensible though it may be, is not.
In addition, we can make a subtler argument. Frank frequently has gotten himself into situations where he might have to kill formerly nonviolent criminals in self-defense, even if those individuals themselves are acting in self-defense!
For example, Frank breaks into Dutton's cell block, kills him and his cellmate, and then brutally murders all the remaining residents of the cell block. While it is entirely possible that the block comprised entirely violent criminals, it is equally possible that it did not, as previously we had seen that some people guilty of white-collar crimes were incarcerated in the same facility. Castle killed all of them in arguable self-defense. But they were acting in self-defense as well: the Punisher had just killed two people in their block. They had good reason to think he would kill them!
Similarly with the Dogs of Hell. He had previously killed some of their members, and after shooting at their motorcycles, looked ready to finish the job. If Daredevil had not stopped him (and the Dogs), he would certainly have tried to kill as many gang members as possible in "self-defense." We can't know for sure whether all those members of the gang, violent though it may be, had previously committed violent crimes. Some might have been too new.
Also, Frank apparently killed the entire Juarez cartel. While most were undoubtedly violent criminals, some probably were merely involved in the shipment or production of drugs.
Tl;dr: Frank will kill nonviolent criminals in self-defense, even they justifiably feel in mortal danger from him. He will also kill people he feels to be complicit in societal problems, such as those who sell child pornography or move drugs for violent criminals.