Hyperventilating until passing out is a bad method, because even if you succeed at fainting, your syncope will be just temporary. Overbreathing reduces the amount of carbon dioxide in the bloodstream, that causes hypocapnia which leads to constriction of cerebral blood vessels and poor delivery of oxygen to the brain. After overbreathing is stopped, your CO2 level goes back to normal (because your cells continue to produce carbon dioxide), and then your brain gets enough oxygen for normal functioning again.
The SWB method relies on reducing O2 in the bloodstream to the point of blackout before CO2 is accumulated to high levels that cause strong urge to breathe or sense of suffocation. Hyperventilation allows you to hold your breath for a longer period, because transition from hypocapnia (lack of CO2) to normocapnia (normal CO2 level) and then to hypercapnia (excess of CO2) takes more time than transition from normocapnia to hypercapnia, so it's possible to consume a large amount of oxygen during long breath holding without experiencing the feeling of air hunger.
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I think that hyperventilation is not needed in case if you breathe helium. When you displace oxygen from your lungs by filling their volume with helium, low partial pressure of O2 in the lungs leads to the inverse flow of oxygen from the bloodstream into the lungs' volume. Then your blood rapidly loses oxygen, so that the blood oxygen saturation drops to the levels at which maintaining consciousness becomes difficult or impossible. Therefore, your goal is to remove as much oxygen from the bloodstream as possible. This can be done by a series of deep exhales and deep inhales of helium or other asphyxiant gas. One cycle of exhale+inhale per 5 - 10 seconds should suffice.
If you have troubles with passing out in 20 - 40 seconds, then it's likely that either your helium is mixed with oxygen or your breathing technique is wrong. In order to achieve complete blackout ASAP, as much air as possible should be exhaled in each exhalation and deep inhalations of helium should be preferred. Shallow breaths with helium are less efficient. Personally, I'd rather use culinary nitrous oxide instead of helium. Nitrous has additional sedative and analgesic effect, and I think that it's never mixed with oxygen in any somewhat signification proportion (due to various technical problems that would arise when storing such a mixture in chargers and using it in cream dispensers).
I think, it's a great method. Simple, accessible, highly reliable (in the absence of potential rescuers), little to no discomfort (if water is not cold).
Passing out doesn't happen immediately. There is a latent period during which you feel yourself normally, then your consciousness gradually fades out for a few seconds till full unconsciousness occurs. When you feel the onset of impending fainting, you can submerge holding your breath.
Helium is not needed to maintain unconsciousness that was already induced by insufficient oxygen level in the blood. The role of helium is to remove a significant amount of oxygen from the bloodstream by means of creating low partial pressure of O2 in the lungs. Once you reached critically low level of O2 in the blood and passed out, your chances to wake up without inhaling fresh oxygen should be very low. And even if this happens somehow, your consciousness and sensitivity to unpleasant stimuli would likely be severely reduced in relation to what you have in your normal conscious state, and the next blackout should occur a few seconds later because you already have profound hypoxia and further oxygen consumption by the body makes it more profound.