So.... my little brain thought about how I might be able to punch the notches out. It's just a triangle - but you can't find a right angle triangle punch - and certainly not one that faces the way you need it! However, a square is just 2 right triangles that got married. :) You just have to turn it a bit. A large square will give you enough 'triangle' to punch out your notches. The one I used has sides that are approximately 1 1/2 inches. Smaller squares may not give you enough 'triangle' for punching.
Here's the paper after it's been cut and scored for an envelope.
Now what you want to do is flip over your punch and line up the corner of the punch just outside your score lines. (I should've use pencil so you could see the lines better but I was hurrying to show you! Oops just noticed a scrap of paper still in my punch!)
Go around and punch out all 4 notches.
Voila! Neater and faster! Just fold up your envelope now. You can always use a corner rounder on your corners if you want to. Or a border punch on the flap like in this post.