Once upon a time there was an evil entity named "hot-side aeration". It was an evil entity that many thought caused beer to taste like cardboard.
Eventually many HBTers united on the inter-webs and discovered that for the most part this entity was powerless against the small size of home brew batches and all was well. Hot-side Aeration was forever banished as a major concern for home brewer.
All was good and the use of mixers to whirlpool wort was declared safe throughout the realm.
I'm over simplifying things but using a mixer is fine, I do it often. There are many threads here dealing with hot side aeration.