The use of hand blenders on egg whites is going to depend entirely on how the whites are intended to be used. This is because the hand blending technique involves inserting a large amount of air into the egg whites quickly.
What Are You Making?
If you are looking to make angel food cake, meringue or any other recipe that calls for folding the egg whites into the main batter, use the hand blenders because you need very high, consistent speeds to get the stiff peaks of fluff with which to fold. The characteristic of this consistency of egg white is that when the blender arm is removed from the mix, a peak of stiff egg white forms in its wake and remains standing. Remember to keep the blender arms in contact with the bottom of the mixing bowl to prevent messy spillover.
For making an omelet, it's not necessary or even advisable to get this kind of aeration in the egg whites, so a hand blender would definitely not be necessary. This is true for any situation that does not require such heavy blending, like making a wash to brush on pastries. In these situations a hand whisker, or even a fork, will suffice for blending the whites.