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A jig saw is for cutting out shapes, but they become unstable and difficult the smaller the material you are cutting. Plus the tighter the curves, the finer the blade you need, which increases the...

To clarify, coping saw to rough shape, rasp to finalize shape, sandpaper to smooth.

One more thing, after you rough them out, while the halves are still attached, you can quickly fine tune the dimensions with a rasp, then when you are satisfied, move to the sandpaper to refine.
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Do not use a jig saw. It is not suited for cutting out small pieces and can be quite dangerous depending on the size of the stock. A coping saw is a few dollars and will zip through the rough shape...

If you have access to a table saw or a band saw, I would recommend ripping your blanks to roughly 1/8 inch first. Even with a disc sander, it takes longer than necessary to get the blanks down to...