Both methods are effective. I don’t like the idea of nails in my wood for obvious reasons. I have used double stick tape but difficult to separate. I use two different methods. If I’m cutting portraits where I need the whole wood blank, I’ll use blue painters tape on the edges of the blanks. If I’m cutting items from the inside of the blanks like ornaments, I’ll use a hot glue gun and apply a bead of hot glue on the edges of the blanks. I’ll usually clamp the stack to keep the edges tight, then glue.
Your cutting is excellent Gary!