While a piece of carton may work for a short period of time, check from time to time whether the you can add a brass or copper seppa to fill up the space. Also check the mekugi whether it has dents and needs to be replaced.
A piece of carton will not be a direct hazard but you should pay attention what your sword has to say. Extra space in the tsuka means that the blade has room to snap against the wood with every strike (and add major stress to the mekugi). This eventually can cause the tsuka to crack.
Hold a sheet of paper against the wall and try to punch through the paper. You will not succeed.
However if you let a friend hold the paper in the air the paper is very fragile and will tear almost instantly.
The wall prevents the paper from abruptly changing it's shape, protecting it from tearing.
The Japanese sword is completely built up from natural and organic materials which are subject to wear. The difference between a strong and fragile sword can as small as a 0.5 mm gap in your handle.