Wildwood -- how can even a small surgical procedure possibly be justified ethically? Are there any health reasons why you need to know the sex? If not, surely this would be carrying out a significant operation just to satisfy curiosity?
What about X-rays?
Or looking at the W & Z chromosomes? Quicker and cheaper than DNA, and could likewise be done from a feather-base.
Or asking another parrot of known sex -- do they not know immediately, and give it away by their behaviour somehow?
European starlings also have the decency to be colour-coded, and they do it even better than budgies -- the bases of their beaks are blue-for-a-boy, pink-for-a-girl.