제대로 한게 맞는건가요?

@Transactional
@Override
public void updatePassword(String UUID, PasswordUpdateDto passwordUpdateDto) {
    User user = userRepository.findByUuid(UUID).orElseThrow(() -> new IllegalArgumentException("UUID정보 없음 = " + UUID));
    user.hashPassword(passwordUpdateDto.getPassword());
}

이게 서비스 코드인데 여기서 예외가 터지면 컨트롤러로 넘어가서 catch (IllegalArgumentException ex) { throw ex } 을 해서 처리하는게 맞게 하는건가요?

@PutMapping("/user/update-password/{UUID}")
public ResponseEntity<String> updatePassword(@PathVariable String UUID, @RequestBody PasswordUpdateInfo passwordUpdateInfo) {
    try {
        ModelMapper modelMapper = new ModelMapper();
        PasswordUpdateDto passwordUpdateDto = modelMapper.map(passwordUpdateInfo,PasswordUpdateDto.class);
        userService.updatePassword(UUID,passwordUpdateDto);
        return ResponseEntity.ok("Password updated successfully");
    } catch (IllegalArgumentException ex) {
        throw ex;
    }

}

@Slf4j
@RestControllerAdvice(annotations = RestController.class)
public class ExceptionController {

    @ExceptionHandler
    public ResponseEntity<ErrorResult> userExHandle(IllegalArgumentException e) {
        ErrorResult errorResult = new ErrorResult("USER-NOT-FIND", e.getMessage());
        return new ResponseEntity<>(errorResult, HttpStatus.BAD_REQUEST);
    }
}

포스트맨 쓰니까 일단 뜨긴뜨닙다