The answer depends on what’s actually being asked: how murch force to accomplish it, or how much effort to accomplish it?
The amount (and type) of force would be easier to calculate, but would still be an approximation based on other similar species we could test it on.
The amount of effort to pull this off (haha) would be a lot harder to estimate and would vary considerably based on the attacker, the victim, and the circumstances. It would undoubtedly require much more effort to do this to an aggressive person who will resist the action while being under attack and great duress than simply the sum of the physical foot-pounds required to cause the trauma. Think about the amount of force needed to squeeze the clippers and cut your dogs nails vs the effort to hold him down and get it done when he’s scared of the clippers and yanking his paws away.
And part of self-defense training, probably the biggest part, is turning the would-be victim into someone who is capable of retaliating. In this sense, the advice of “Go for the balls” might even be productive, since it carries the message “If someone’s trying to rape you, it is fully acceptable to retaliate to the fullest extent possible, up to and including the action that the rapist will find most horrific”. It can only be slightly improved by amending it to “Go for the balls, and everything else you can reach at the same time”.
Probably, or nearly so. But the reason they defend both so instinctively is that a successful attack on either is probably going to be incapacitating. And it’s hard, even instinctively, to defend both at once, so if you attack both at once, there’s a better chance at one of them going through, and you don’t much care which one.