The risk you're running is moisture, leading to rust. Firearms tend to be less susceptible to rusting if they're stored in such a way that dry air can circulate around them and they don't go through wide temperature swings which would encourage water vapor condensing on them.
Soft cases are for transport, primarily. As they press against the metal, they can hold moisture against the metal, and then you get very concentrated points of rust, even to the point of pitting.
You can get various protective, breathable "gun socks" which may be better than soft cases for long term storage, but the best option would be a rack where they can stand and get air around them.
As far as a plastic case goes, I don't see a problem with that, aside from possibly trapping in moisture, again.
If this is the best you can do, there are worse things. Keep the box in a climate-controlled, dry place. Take them out and wipe them down with oil frequently so you can catch corrosion problems as early as possible.