applying shellac by hand is a problem. Try rattle can shellac and don't touch until completely dry.
I use Sherwin Williams Chem Aqua Plus lacquer via air spry gun and don't touch the pieces until dry.
I lay the puzzle pieces on bump-ons in a strip of wood 3" x 4'. The piece of wood rests on a lazy susan device so it can be rotated with ease to coat all ends and a surface.
After the initial coat is dry, I will flip the pieces and recoat the edges and the uncoated surface. I do all of this outside on a deck.
Unfortunately the Sherwin Williams product only comes in a gallon - no rattle cans.
You might consider a water based sealant made by Deft that comes in a rattle can.
https://www.amazon.com/Deft-Interior-Water-Based-11-25-Ounce-Aerosol/dp/B0017OKFQ2
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