Johnson & Johnson's Band-Aids are available in Skin-Flex type, either a straight strip or a butterfly type with the dressing pad running from the middle to one side, it's intended for knuckles & fingertips. This latter type is quite suitable for the dermatitis-affedcted right palm.
As the name suggests, the fabric is thin & flexible yet the adhesive is strong & water-resistant. They're quite capable of staying in place for two days, even surviving a couple of hot 10-minute showers.