Well, you have to be careful with the terminology here: Once you add skewness and kurtosis, the distribution will no longer be "Gaussian", right? Basically, you want to generate random data, that, after infinite sampling forms a predetermined (non-uniform, non-normal) probablility distribution shape.
You probably could generate a inverse probablility function from your desired distribution, then feed it with the 0...1 uniform distribution.
As an example, I show the image of a VI that uses the Inv-normal function (found deep in the probability palette) to generate gaussian distributed random noise from a uniform noise distribution. I am sure you can adapt the same idea to generate data that conforms to your desired statistics.