Because you ask "Which butt plate for a thin stock?" I must assume you don't have a Track of the Wolf Catalog.
These don't cost a lot and they are invaluable in determining not only what is available, but exactly what size and what shape the parts are.
With all of the gun hardware like locks, trigger guards, butt plates, triggers, the pictures are Full Size. That means you can measure the picture and know what your getting.
Obviously, if your stocks butt is 1 1/8 wide, you don't want to buy a 2 1/4 inch wide butt plate so, by all means, buy a copy of this book. It is worth every cent.
Also, I would suggest that unless the picture in the book is almost exactly the shape you want, you buy one of the sand cast butt plates.
The Investment Castings are often made out of Bronze and if you try bending them they will break.
As for fitting, as LeatherMoose mentioned you need a saw or a course file or rasp.
If you get a brass buttplate, you also need a big hammer and a block of wood.
When the stocks shape is very close to matching the plate, you can use the wood to protect the plate while you pound it into shape with the hammer.
For final fitting, I use inletting black and a small file or sandpaper block to remove the wood that is preventing a perfect fit.
