Some of you may (or may not) know from reading past posts of mine that I tend to choreograph my fight scenes (sword fights) I also do that to regular hand-to-hand scenes although I do not have a pugilistic background but I did take karate for many years (probably have forgotten enough to make myself extremely dangerous to myself.)
There are things I see in written fight scenes that usually make me sit back and wonder and know that the writer is not all that familiar with fighting. (I'm sure I've written more than one or two also)
For instance, yes, a short, petit woman can get a good nose bleed punch in against a bigger guy. I know, I did it to my sensei during a demonstration.
However... depending on what you're going for, the better punch (in my opinion) for a shorter person, man or woman, is the throat punch. Why? it is natural, when one has something flying at one's face, to turn your head. If it's flying at you from under you, you not only turn your head but you throw it back, exposing the throat.
The throat is a soft target that allows a hella damage. It also doesn't hurt (much) the defending person (or attacking). The face is a hard target and hurts like hell when you hit it, maybe not at the time depending on your adrenaline but trust me, it will. The same thing with putting fists through walls etc. (2 broken knuckles on a makawara board taught me that lesson)
Advice from the sensei,
1. don't punch the shoulder, punch through the shoulder.
2. Don't punch and see if it was effective, keep punching (that's just logic)
3. run when you can
I have a favorite punch that, yes, I have used in a real life situation more than once. (I used to bartend at a sweet little tavern next to a biker tavern but the biker guys looked out for us women bartenders in my tavern.)
Anyway... I call it the "George Gently" punch and you can do it either with fist or elbow. "George Gently" was a British police detective TV show. He was a short little guy and had a signature punch. It is, in boxing, an illegal move. It is .. tada A kidney punch. A woman's sharp little elbow and smaller fist, if your protagonist is a woman, can do some laying out of the bad guys with that punch. Delivered by a big guy and your opponent is usually out for the count.
The thing about these two punches are they are easy to describe and usually invoke a reaction in your reader, although not as visceral as a kick up the middle.
Pushing is a hard thing to do in a fight unless the other person is:
1. already off balance
2. has something behind him to get him off balance
3. you can hit him in the center of his gravity
4. drugged or drunk etc. and that's a whole new problem because they might be too relaxed.
A Calgary Flames hockey player was hated by a lot of opposing teams for the fact that, at 5' 6" when up against 6' 2" players he could knock them on their butts because he was at the right height to get them in their center of gravity and knock them off their feet. Person in question: Theoren Fleury.
If you're not familiar with writing fights etc. I hope some of this information helps. Also, sometimes it's fun to give your protagonist a "signature" punch.
Write hard, write true