The top step is not a tread. It's flooring. You buy the stair nose as part of your flooring purchase, not the stairway build. Most manufacturers of hardwood will provide a matching stair nose, but you may have to order it.
![enter image description here](https://i.stack.imgur.com/WNiLs.jpg)
Note that the stair nose is a groove. You can also purchase a double-tongue that will slip in that groove converting it to a tongue should you need to.
There are 2 ways to do this, the first way is in essence just cutting the wall at the top of the skirt board and capping it off and setting the handrail on top of the cap that is finishing off the cut wall, sounds a bit crude, but essentially that describes what you will have.![enter image description here](https://i.stack.imgur.com/50aDg.png)
![enter image description here](https://i.stack.imgur.com/gY9z6.jpg)
The up side to this is you will not need to do a floor repair, depending on where your wall ends where the newel will be.
The other way to do it is by removing the wall entirely, repairing the floor, removing the treads and risers, and set longer ones with return nosings on either side. and re-support the stairs with a new walls under the existing carriages.![enter image description here](https://i.stack.imgur.com/sREfx.png)
![enter image description here](https://i.stack.imgur.com/6kdwk.jpg)
This is the most work, but will give the best result in my opinion.
Jan. 2, 2014 edit
Here is the work I did in 1989 that shows what I did.![Stair1](https://i.stack.imgur.com/kiybG.jpg)
![Stair2](https://i.stack.imgur.com/sfhJj.jpg)
This one shows the best example of the effect I was trying to explain. I do not have a shot that shows how the handrail goes past the ceiling, but with a little imagination you could picture what the rail would have to do if the stairs were much wider at the bottom.![Stair4](https://i.stack.imgur.com/2sAZB.jpg)
![Stair5](https://i.stack.imgur.com/vOgza.jpg)
Edit #2
I did a little calculating to help, if it may![enter image description here](https://i.stack.imgur.com/cpBZs.png)
Best Answer
Yes you can add 1/2" plywood to all carriages/stingers to make up the 1/2" difference. Glue and a few small nails to hold it in place while the new treads go on is all you will need. Do not spare the glue/construction adhesive.