Oracle - drop table constraints without dropping tables

You can do it with dynamic SQL and the data dictionary:

begin
    for r in ( select table_name, constraint_name
               from user_constraints
               where constraint_type = 'R' )
    loop
        execute immediate 'alter table '|| r.table_name
                          ||' drop constraint '|| r.constraint_name;
    end loop;
end;

If the tables are owned by more than one user you'll need to drive from DBA_CONSTRAINTS and include OWNER in the projection and the executed statement. If you want to touch less than all the tables I'm afraid you'll need to specify the list in the WHERE clause, unless there's some pattern to their names.