An enzyme is not alive, the beekeepers use a lot of metal in getting your honey out anyway. They use a metal knife to decap the wax and there is metal in a spinner.
Enzymes are proteins that act as biological catalysts by accelerating chemical reactions. You can't "kill" them.
So metal spoon is fine? I'm no expert but I realised in Greece they always use special olive tree wooden spoons for honey.
In Italy is also quite common.
This "honey dipper" tool is handy to put the correct quantity without touching the food, just rotate it to stop the flow.
But I never heard that a metal spoon can ruin the honey.
I checked with a beekeeper I know irl, he confirmed the spoon thing.
