Should I store ZipCode on Storage?

I'm working on an e-commerce website and there is the zip code field (in Brazil we call it CEP) that is a data that can be very usefull, for example, I can get most of the address information (city, state, location, street name) and also calculate the shipping cost to that address.

So imagine the user is a guest on the website visiting a product page and type the zip code to get the shipping cost for that product. I assume (also as a user) that it's ok to store the zip code and, if I want to get the shipping cost for another product, the zip is already on the form.

So my question is, should I store the zip code on the storage? Or let the user type it everytime he wants to get the shipping cost or create an account?

If it's ok to save, then where should I save it? SessionStorage, LocalStorage, cookies? I'm afraid to keep the information too much time (LocalStorage/Cookie) and give a sense that the webpage is getting user's information behind the scene.