that's how I made plum bows from similar thickness staves: cut with table saw.
However, now you will want to peel off the bark, and maybe even rough out the bow shape, or the stave will split through the center and/or create random spiraling checks. Been there, done that.
When you've peeled off the bark (and sealed the ends really well), store it in a dry but not warm place, so it can dry slowly. Or rough out the bow shape immediately, and measure the moisture loss (mass loss) every day until it's stable (can take a month or so).
Since you don't have that much thickness left at the handle, either glue a riser (which is hard without adequate tools to flatten really well the surface), or make a shorter bow that bends a little through the handle. Apple is amazingly flexible wood.
Joachim