You don't need to breathe too hard into the individual's mouth. Just enough to watch the chest rise and fall. A normal breath, which lasts about a second, will be perfectly adequate.
If anybody starts mithering that you're doing it in the wrong order, just ignore them.
I'm telling you the ABC (Airways, Breathing, Circulation) method, but there's been a massive campaign by the American Heart Association to go for CBA (Circulation, Breathing, Airways) instead. As far as I can ascertain, that's largely because people were so busy worrying about looking like they're snogging a stranger, that they talked themselves out of performing CPR.
Starting with chest compressions meant they were committed before they got to the socially impolite stage, thus were less likely to back out.
Other campaigns, like the Hands Only CPR one across two continents, took out entirely the requirement to give rescue breaths. It was hoped that more people would prefer to save lives that way, instead of fretting what other people were thinking about them.
In short, various people learn different ways to do this. As long as you're doing one of them, it really doesn't matter which one!