If the pull start casing and screw locations map out to a perfect square, then you can rotate the pull start the 90 degrees you desire. Its operation will not be affected in any way other than the direction the pull chord plays out when you give it a pull.
As for tips on removing the one way or trying to keep the spring from coming undone, there really aren't any. When you remove the screws that hold the pull start casing to the engine, you should be able to remove the pull start without the spring coming undone. The one way should either remain on the shaft or in the case it "sticks" in the pull start should just come out with some gentle prodding.
If you are worried that the spring might undo itself, you can use a flat head screwdriver or other flat metal tool to slide behind the pull start casing as you remove it. The object is to keep the chord spool inside the casing.
The only time I have had a pull start spring undo itself was when the spring had already snapped. Since it was already broken, when I removed the pull start casing it just finished its unwinding and went everywhere.