Best way to tame flyaways from a French braid?

First off, I know absolutely nothing about hair products. Second, I have thin hair that gets greasy easily. I braid my hair for softball because it's gentler on my scalp than a snug ponytail. I need recommendations for flyaways from my braids. I don't care about the rest of my head; I just want the hair around my ears and forehead to stay down. I currently braid my hair and spread some mousse on after but it doesn't really look natural and it's kind of weird looking.

I'm also looking for something that is non greasy. Something that doesn't guarantee I have to wash my hair later. The mousse I use hardens up but I can brush it out. Also, I wear a visor so it needs to be something that withstands me moving my visor back and forth.