A shallow (also known as Zero-Copy) clone only duplicates the metadata of the table being cloned; the data files of the table itself are not copied. This type of cloning does not create another physical copy of the data resulting in minimal storage costs.
Thus, if you do not have the MODIFY permission on the source table, you will not be able to create a shallow clone of that table.
You can try either copying with a CTAS command or Deep Clone, and check if its helpful for your use case