Yes you can use an electric hand mixer with one beater attachment on it.
I've used my electric hand mixer with one beater attachment when all I could find was one of the beater attachments and it worked just fine.
Although the electric hand mixer will do much better if you do use both beater attachments as it will mix the ingredients much better and faster.
But if you want to or need to use the electric hand mixer with only one beater attachments you certainly can.
Also another good use for an electric hand mixer is a paint mixer.
However don't use the same electric mixer and attachments for paint and food have a separate electric hand mixer for the paint and one for the food.