I got it. We built a new stored procedure as a wrapper around the one with a cursor like this:
PROCEDURE sp_run_sp_with_cursor
AS
define variables here (int);
BEGIN
schema.stored_proc_with_cursor(cursor_variable,other_variables);
FETCH cursor_variable INTO other_variables;
WHILE cursor_variable%FOUND
LOOP
DBMS_OUTPUT.put_line('variable name: ' || variable);
FETCH cursor_variable INTO other_variables;
END LOOP;
END sp_run_sp_with_cursor;
Then we made it return a comma delimited list of the values we need.