I've done some mine delving and I've amassed a selection of equipment that's frankly useless to me; some outdated weapons, shoes, and rings. While I know that I could dispose of them with the inventory trash, I would prefer to sell them. However, I can't put them in the shipping box.
It is possible to sell your unwanted equipment to the General Store (Pierre's) or any other NPC shop such as the Adventurer's Guild.
This page on the Wiki also gives you a buy/sell price for each weapon/type you want to sell.