How can I fix a stair to its shape?

You can lock the corner blocks into various block states (e.g. inner_left, inner_right, etc...) by tricking the logic as you position blocks. You can do things like this:

In general, start by adding a stair block, then another next to it with the same orientation. Finally, orient yourself 90 degrees to add the third stair which will complete a corner. Next delete the first block you positioned and the corner block should keep its state. It gets tricky to position corners near each other and takes some practice.

I first got this idea from practicing making a hot tub like this:

Hot tub and Beach

I'll try to make a video on the techniques.

Yes! It is possible only by copying and pasting a corner stair with world edit, though.

I know most people are going to think that I'm just necroposting on a 6 year old post, but I think plenty of people end up seeing this post and I happened to find an answer!

First, I want to note that this can only be done in Creative, but you can switch your gamemode back to survival and it will still be there.

The first step to doing this is by creating a new Creative world or switching your gamemode to Create via cheats. The cheat to do this is /gamemode creative and simply type this into the Minecraft text chat. Once you're in Creative you will need to give yourself the Debug Stick by typing the cheat /give @a minecraft:debug_stick. Now you're ready to change the shape of a stair!

Place down your stair wherever you want it to be as if you break it or place a block next to it you will have to repeat the process. Now hold out the Debug Stick and left click (M1 on PC) until it says "selected "shape" (straight)"

After that simply left click until your desired shape is chosen.

You can now put your stuff away and the stair will stay in that shape as long as you don't break it or place a block next to it.