Cut-cell meshes provide an efficient way to create accurate approximations of geometries at the cost of having very irregular mesh elements, in particular arbitrarily small elements, leading to the so called small cell problem. In the hyperbolic setting with explicit time-stepping schemes, this makes it infeasible to select an appropriate time-stepping size. We want to consider how one can formulate additional stabilization terms for a discontinuous Galerkin discretization which lead to stable updates on small cut-cells and a corrected domain of dependence on their neighbor elements.