It would be interesting to read the whole article that you quote, I have to say that I agree with the general thrust of it, whilst disagreeing with the female/male distinction. Saying that, similar problems can arise with male/female interactions whichever is in the position of authority, we are just better at "reading" signals from our own sex. I find it much easier to calm down an irate man than a woman.
In conflict (using the word in its loosest sense) there should be an gradual escalation, and you should always leave a way out that saves "face" for the other side. Also it should be kept in mind the end result that you want, and an open mind should be kept about how you get there.
Just from a body language point of view, if someone is standing and you are sitting, you immediatley feel on the defensive, and a certain amount of fear, which can raise the tension.
In the situation above a potential solution would be to involve another (imaginary) passenger.
CC: Gentleman, wonder if you could help me out, we have a nervous passenger aboard an your singing is making her uncomfortable, could you stop so that we can get on with the safety briefing and get her and the rest of the passengers off on holiday as soon as possible?
You are taking advantage of the typical male reaction to want to help woman in distress, getting in a mention of the primary purpose of the CC (safety) and reminding them that this is not the holiday but the means of getting there. Once you have got their agreement, they would need a reminder that you and the rest of the crew are the ones in a position of authority.
perhaps (slightly jokey manner) CC: because I'd hate to have to throw you off the aircraft!
If they continue (unlikely), because of the previous conversation you have established yourself as the one in authority, and they have accepted it, so you can be very firm and they will accept that they have been warned previously and so should have been on much better behaviour.
Everyone has seen this sort of thing in action, the person who can control seemingly any situation, the trick is to find what works for you, and know where your strengths lie, it is the result that matters.