Get a bunch of these tunes under your belt, and then you can try jigs and reels. Start by finding tunes that lay right for a basic 5-finger position, look through books, or figure a couple out by ear. With a bit of searching, you'll find an easy tune that you can really crank on. There are plenty of them. I played English Country Dance music for years 2-handed without ever giving a thought to applying that skill to contra dance music.
Most English tunes are very accessible for piano fingering.
Just play with your right hand until you feel comfortable with the feeling and the sound. Don't worry if you can't get it up to dance speed. Playing the piano is just different, and it's no shame to play more slowly. But if you get really good at a tune at a comfortable tempo, you'll find you are able to play it faster than you think you can. Now add your left hand.