Oracle 21c

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ALTER SESSION SET NLS_DATE_FORMAT = 'YYYY-MM-DD HH24:MI:SS';
CREATE PROCEDURE EXECUTE_AND_IGNORE_ERROR(
  dmlStatement IN VARCHAR2,
  oraErrorCode IN NUMBER
) AS
BEGIN
  EXECUTE IMMEDIATE q'{DECLARE
    possibleException EXCEPTION;
    PRAGMA EXCEPTION_INIT (possibleException, }' || oraErrorCode || q'{);
  BEGIN
    EXECUTE IMMEDIATE :1;
  EXCEPTION
     WHEN possibleException THEN
       DBMS_OUTPUT.PUT_LINE(
         'Warning: Ignoring error [' || :2 || '] after executing [' || :3 || ']'
       );
       NULL;
  END;}'
  USING dmlStatement, oraErrorCode, dmlStatement;
END EXECUTE_AND_IGNORE_ERROR;
/
SELECT * FROM user_errors;
BEGIN
  DBMS_OUTPUT.ENABLE();
  EXECUTE_AND_IGNORE_ERROR('INSERT INTO does_not_exist (id) VALUES (1)', -942);
END;
/
1 rows affected

dbms_output:
Warning: Ignoring error [-942] after executing [INSERT INTO does_not_exist (id) VALUES (1)]