Day for night works best midday when the sun is directly overhead and mostly on a clear day. The effect is moonlight which is direct or near direct toplight usually. Not very sidey except when it's coming through windows mostly. Since you're doing black and white, you're only key to people of the time and day is the contrast ratios and the elements in the frame like practical lights. You can't play with color contrast the way most films would.
If it's overcast and you have a very softlit look, that's rough. It should look more hard. And if the sun starts setting and becomes a bright low angle key it'll probably look odd cause moonlight doesn't look like that.
But I don't know your locations or any details. Those are just general tips. The trouble is day for night when there's no color contrast and no practicals. That's always the dead giveaway. You're shooting black and white so that will help. However there is still the issue of practical lights.
For example, if you shoot in a city and the streetlights aren't on and the cars aren't using headlights and what not, the audience might think it's weird looking. But if you're in the country it's less of an issue. I would still keep it in mind and try to make it look like people have turned on lights because it's dark out.