Can I remove traps from my Stonewood base and get the materials back?

Try the pick-up option on one trap before changing the whole setup. Check what the game returns to you, since recovering the trap itself and getting back all the materials used to craft it aren’t necessarily the same thing. Then you can decide whether to move the rest or leave them in place.

You can adjust your storm shield setup as you learn what works, so there’s no need to tear everything out at once.