In New World, there are no NPCs that will give you coins for the unwanted items in your bag. The only sensible way to remove weapons and armor from your inventory is to salvage them. This also makes sense because it gives you repair parts as well as materials. You’ll need them to repair your equipment.
To disassemble a weapon or piece of armor of your choice, open your inventory and hover the mouse over the item. Then press S and click once, confirm your wish for destruction with E and it’s salvaged.
You can also Quick-Salvage it by pressing STRG + S + Left-Click. You then don’t get a Confirmation Dialog.
If you are someone who likes to click, you can also click on the item in your bag, bring it into focus, and then click on Salvage without using your keyboard.