You should just be able to use
Alter table Employee drop primary key;
and then
ALTER TABLE Employee ADD CONSTRAINT pk_empid PRIMARY KEY (EmpId);
I would not have expected
drop Index
to delete any data - perhaps you fell foul of this note from the documentation
Quote:
When you drop an index, Oracle Database invalidates all objects that depend on the underlying table, including views, packages, package bodies, functions, and procedures.