

Have you considered an electric shaver? It doesn’t cut as close, but by the same token, it also doesn’t scrape across the skin. You’ll avoid catching the tops of any spots that you may have, and until your skin becomes happier with wet shaving, it’ll keep the whiskers away.
I think this is the key. If the plane’s going anyway, the additional environmental impact of you being on it or not is essentially moot.
As for whether the plane should be flying in the first place, well obviously not.
If it helps you rationalise it at all, if anything you’re making the plane more efficient by essentially halving your friend’s carbon footprint.