Rollei made the "Rolleinar" accessory close-up lenses for their TLRs, so if you really want a close-up, that might be an option.
Otherwise, for handheld capability, minimal-to-no mirror slap, and macro/close-up capability, I'd say a Mamiya C330 TLR would fit the bill. In addition to being a TLR (so no mirror slap), it has integrated bellows, so you can get quite close-up. It also supports interchangeable lenses, with the 180mm lens being popular for portraits. The leaf shutters on the lenses tend to be pretty quiet as well.