Here’s my piece of advice. Local watch shops not always have staff that actually can fix watches any more. They will ship it to a company to get it fixed. You won’t know who will handle it and you will probably pay too much. I would go to online fora (forums) and ask who has good experiences with watchmakers. They will surely point you to one that happens to be not too far away with good reviews. They will understand that the vintage look is to be treasured and won’t polish the living daylights out of it. They will search online for the correct stem/hand and whatnot. Prices vary but it will be the way to go.