What is the best practice to save mean and std in model?

Say I have trained a model with some normalized train data. When inference, I need the same mean and std of the normalization. Naturally, this mean and std are stored in my data module which is not included in the checkpoint.
Now I have to put the mean/std in my model as 2 parameters of ini in which I call self.save_hyparameters() to save them.

Any suggestions?

A drawback of this flow is that: to get the train data mean and std, I have to do this

my_data_module.prepare_data()
my_data_module.setup("fit")

before creating my model.