It is indeed possible.
In your general shipping rates (it’s the default shipping profile), all products are added by default (unless they are assigned to a custom shipping profile). So in this profile, you need to set the shipping rules that can apply to all these products. If your “frozen products” are not eligible to any shipping bar local delivery & pickup, then you should have no shipping rates in here.
Then, you should see something like this and can create a custom profile right here:
In this new profile, you can add manually all products that are eligible for shipping (all products except “frozen products”) and add the shipping rates. This way, if a customer add frozen products, he won’t see any shipping method except local delivery & pickup if you have set it up correctly.