This is actually a pretty tough question- because, as far as I know, most cartoon characters are ambidextrous as it makes animating easier, and remembering which hand is the dominant hand, especially in a more action-y scene, is difficult.
So, if we look at these pictures of Harrison-
These either show him directly using his left hand, or indicates he does use it (the spoon in the potatoes is on the left side).
show that he’s more than capable of using his right hand. He can even shoot fire out of it.
And of course, he can use both easily.
In conclusion Harrison is ambidextrous thanks for coming to my TedTalk
1. KANA - BOON - Baton Road. Overtaking the distance, our sky-blue days are covered in wounds. Faced with uneasiness and beaten paths on this Baton Road, We’ll sometimes trip along the way. But even the seeds planted by our tears will bloom into magnificent flowers to hand down - ! Keep growing it with those seeds; your future - !
2. Amazarashi - Sora Ni Utaeba. Cutting through falsehood to gaze upon the blue sky, eternity is in flight - ! Singin’ to the sky, Your voice was screaming soemthing that day: things you wanted to say and things you couldn’t. Singin’ to the sky, we’ll take even our regrets along. It’s inevitable, it’s inevitable: We lost too much to put an end to it here. So keep up the fight - ! They’re finite, they’re finite: We have precious few futures left. So keep up the fight - !
3. Hatsune Miku - Hello, How Are You - ? Hello - ! I think that kind of person appeared only in old anime. How are you - ? I am so jealous, that someone can be loved by all. Sleeping … I must stop saying silly things and start preparing. Crying … In order to hide my tear marks.
4. LiSA - Rally Go Round. In this Falling Star, Revolving, Roulette, Rally Go Round. (You are the player.) So stick to the heart-shaped directional arrows - ! (You’re my love.) I’ll take my strongest, biggest love in the palm of my hand, And help push you along, so send it flying with all your might - ! (Don’t miss your big chance - !)