Hoping you can tell me, is wireless bra healthier than one with wire / bar at the bottom?

Not if it fits : Comfortably. A book called “dressed to kill” indicated underwire bras restricted lymphatic drainage & led to accumulation of toxins in the breast. It was theorized led to development of breast cancer. However, lymphatic drainage from the breast is not downward (gravity) – it moves towards the axilla (arm pit). The author's conclusions were not based on medical science & are not deemed accurate.