I am not entirely understanding what your suggested approach is, but I will try to provide a few comments. You can simulate the model solution of the linearized standard model using the simult_ function, see e.g. [Normal AND Non-Normal Random Variables)
What you have to ask yourself is whether your model solution from the linearized model is correct. First of all, the model needs to be differentiable. If that is the case, Dynare approximates any shock distribution by the first two moments, i.e. effectively a normal distribution. However, at first order, we have certainty equivalence. Thus, the variance of the shock process does not matter (as do higher order moments). Rather, only the mean matters. Thus, you can basically use any shock distribution, but you need to be aware that by construction, the higher order moments will not affect the solution.