Or, to paraphrase, all you need is a corset,
A corset will provide mechanical counterpressure for your breathing, but there are a lot of other ways in which vacuum (or near-vacuum) exposure can hurt you that mean you need to cover up. Renan already referenced the main thing I was going to, which was Kittinger's hand. It didn't cause permanant damage, but it was repressurised swiftly. How much more pronounced the effects will be in a harder vacuum is probably unknown, but it seems reasonable to assume that exposed bodyparts will swell and bruise and be largely useless... without counterpressure on your hands, you won't be able to operate any sort of controls, for example.
And that was just his hand. There maybe other parts of your anatomy that you'd rather didn't suffer 100% bruising and traumatic swelling. Human skin is quite tough stuff, which is why people are unlikely to explode, Hollywood-style, on exposure to vacuum. There are numerous gaps in your skin though, allowing internal plumbing to communicate with the outside. Vacuum exposure to those, especially with any sort of counterpressure on the torso, may result in unpleasantness like your viscera extruding itself through the hole.
There's also stuff like aerogastralgia (something that's annoyingly poorly documented online, at least this side of a paywall) caused by air bubbles in the stomach and digestive tract expanding and causing pain (but rarely damage). Intense abdominal cramping is likely to hinder escape efforts. Kittinger had a special diet leading up to his high altitude jumps to reduce the probability of gas formation during digestion, but suitable lower-torso counterpressure should avoid this sort of issue.
Your mask will need to be well sealed against a ~one atmosphere pressure difference, and cover the eyes, nose and mouth. It'll need to seal well against dirty, sweaty skin and hair. This is at least just a simple matter of engineering, but it will be more like a hood than a mask by the time you're finished.
Failure to protect the eyes will probably result in at least temporary blindness, but there doesn't seem to be a lot of information of eye-vacuum exposure. The surface of the eye will dry out very quickly, and tears will rapidly boil away before performing any useful wetting, so the only thing the victim can do is keep their eyes tightly shut which will impair escape attempts.
Failure to protect the ears may result in ear damage, depending on how quickly pressure dropped and how sensibly the victim reacted. The Divers Alert Network has a whole section on ear barotrauma, none of which is good news. Effects like (possibly permananent) deafness probably won't bother them at the time, but inner ear damage can cause serious dizziness and vertigo which will definitely make any further escape attempts much harder. Eardum damage can also result in nausea and vomiting, so if that does occur and you don't have a good way to keep the breathing mask clear, the victim will drown in their own vomit.
and high heels.
Whatever floats your boat, but I haven't noticed those gracing the uniforms of any firefighters.