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Pick up an old Smoothing hand plane, I see them in flea markets all the time for 5-10 dollars, may be a bit rusty. A No. 3 or 4 or even a block plane will work in a pinch for the width of wood you will be working with.
Hone up the iron, you can plane them to the thickness you need in a couple of minutes.
Before there was machinery, folks used hand tools… some still do.
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It's hard to get the right size wood for scales. It's either too short or too narrow or too fat or too thing. The best solution I've found (before I had a bandsaw) is to get 1x1 turning blanks. They'll pretty much accommodate any scale shape. You can rip them by hand with a Japanese hand saw and cut out the shape with a coping saw. Together, the saws are about 40$ on the high end.
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To the O.P,If you have a woodcrafters store near you,Take the blanks in,they will run them thru a bandsaw for nothing.