Dealing with a-holes by learning how to beat them in a fight is like learning to cross the road by waiting until you get hit by a car and then doing a stuntman role over the bonnet. You don't ofcourse do that, your road safety is about learning the skills to cross the road in such a way that you reduce as much as possible the chances of being hit by the car.
Same with SD, whilst physical skills are necessary they are not the largest slice of the cake. The majority of SD skills of soft skills (i.e. Non physical). For example, I don't deal with "eye contact challengers" by waiting until a fight starts and then hoping my fighting skills are superior. I deal with eye contact challenges when they first look at me, so they realise I am not the victim they think i am (I'm small too, 165cm) that way move on and look for someone who displays the victim body language they are looking for, thus reducing the prospect of it developing to the stage where I have to fight.
Martial arts classes will give you the hard (physical) skills, but won't give you the soft skills that make up SD. I would suggest getting Dead or Alive: The Definitive Self Protection Handbook, by Geoff Thompson, which will help you with the soft skills that Martial Arts classes won't cover.