Ok, it's not stylish or beautiful, but I saw a 'thing' in one of those newpaper inserts. It was like a small shrug type garment, to be worn underneath a vest top to cover scary arms. It was quite tight and fitted/clipped together under your bra.
I have no idea what it/they are called and where I might buy one? It basically just adds short sleeves to your top without the bulk/heat of wearing a t-shirt.