I've done some mine delving and I've amassed a selection of equipment that's frankly useless to me; some outdated weapons, shoes, and rings.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 Adventurer's Guild once unlocked.
This page on the Wiki also gives you a buy/sell price for each weapon/type you want to sell.
Pierre's Shop and the Adventurer's Guild will take your equipment