If I were you, I would try my best to overcome the apprehension and do it without plugging your nose. A common technique to help with that is to breath out through your nose ever so slightly so that the air bubbles form a sort of plug.
The point of that float is to remain calm and consume as little energy as possible, as a survival technique. If you are using one hand to plug your nose, then you are going to have to expend that much more energy to stay afloat. Unless you just naturally float really well, most people have to move their arms and legs just a little to keep oriented. Doing it short one hand will not be easier, and judging by what others have said if you move too much you will get yelled at.
I have to ask, are you ok swimming underwater without plugging your nose? Because if so, how is this functionally different?
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