First: how little pressure can a human cope with? The Armstrong limit is 0.0618 atmospheres or 60,000 feet altitude. Water boils and we can't have that in our lungs.
At lower pressures the amount of oxygen, even pure oxygen, is not enough. From the above linked article.
At 11,900 m (39,000 ft), breathing pure oxygen through an unsealed
face mask, one is breathing the same partial pressure of oxygen as one
would experience with regular air at around 3,600 m (11,800 ft) above
sea level. At higher altitudes, oxygen must be delivered through a
sealed mask with increased pressure, to maintain a physiologically
adequate partial pressure pressure of oxygen. If the user does not
wear a pressure suit or a counter-pressure garment that restricts the
movement of their chest, the high pressure air can cause damage to the
So we need oxygen under pressure. That is what your space face mask would deliver. Doable?
Pressure in the lungs requires a balancing atmospheric pressure as delivered by a pressurized suit, or by the column of air towering over my house. If you just pump pressurized air in to the lungs, the pressure differential causes barotrauma . Barotrauma happens to people on ventilators when air under too much pressure is used (in an effort to overcome stiff sick lungs and get the O2 in). Barotrauma can happen when a diver breathes pressurized air at depth and then ascends holding breath. The pressurized air in the lungs, no longer balanced by an equal external pressure from the outside water, expands in the lungs. Your chest swells as your lungs increase in size. Hopefully you exhale and let it out! Too much and the air bursts out - either into body tissue spaces outside the lungs or into the bloodstream. That last is an air embolism which can kill or cause a stroke.
But positive pressure ventilation is definitely used, all the time. People on ventilators are often ventilated with air slightly above atmospheric pressure: this is positive end expiratory pressure, or PEEP. It is related to continuous positive airway pressure or CPAP which people use at home to prevent sleep apnea.
So we can breathe pressurized air. Barotrauma occurs when the pressure is too much over ambient. On a ventilator 20 mm Hg PEEP (20 mm Hg over ambient pressure) is when it really starts getting to be too much. Could 20 mm Hg pressure in the space mask deliver enough oxygen? From the above, 39000 feet is 0.19 atmospheres pressure, which is 144 mm Hg. Breathing that much unopposed pressure you would pop.
If only there were some way to make the effective oxygen concentration greater than plain oxygen gas, which you have to have under pressure to get enough in there. Gas is so gaseous. Could one achieve adequate O2 concentration at a very low pressure with some oxygen carrying liquid like perfluorocarbon? Breathing oxygenated liquids is called liquid ventilation. Maybe the system would flood the lungs and face mask with an oxygen carrying liquid, and on reclaiming it into the reservoir with exhalation oxygenate it a lot under pressure / remove CO2, then allow the user to inhale the liquid again.
The Armstrong limit above is 46 mm Hg and so even with the liquid ventilation, body fluids would still be boiling and that has to be bad.
I would like to have this work somehow but I think your people are going to need pressure suits. They can be very sleek, form fitting suits like speed skaters wear. You can put some people wearing them on the front of your paperback.