Performance Tuning :: Slow Join Between Dba_tab_cols And Dba_types

The product I work on requires a query to tell us what tables are dependent on certain types.

SELECT dba_tab_cols.owner,
dba_tab_cols.table_name,
dba_tab_cols.data_type_owner,
dba_tab_cols.data_type
FROM dba_tab_cols
JOIN dba_types
ON dba_types.owner = dba_tab_cols.data_type_owner
AND dba_types.type_name = dba_tab_cols.data_type
WHERE (dba_types.owner IN ('SCHEMA1', 'SCHEMA2'......))

I find this query to be pretty slow. I think it is because data_type_owner in dba_tab_cols is not indexed. Adding an index is not an option because users expect our product to read-only.