Shooting and ball handling have nothing to do with arm length or hand size.
Most of your jump shot is elbow through fingertips. It is mechanics, making your shot simple and repeatable, and practice.
The dribbling is probably a remnant of being a guard growing up. Big kids get stuck as centers and don't have to dribble, therefore they don't get good at it.
I have no concerns about arm length. I do have some mechanical concerns. Olynyk doesn't shoot the ball from an especially high position, has little arc on his shot, and has it out in front of him a little. Those are the jumpers that are easy to block so I do expect him to struggle with that when guarded by really quick long leapers on the perimeter. They are also the jumpers that are most consistent. A good example of this is Matt Bonner of San Antonio. Very good, consistent three point shooter, but he has to be wide open to get his shot off. He is much more extreme than Olynyk however.
His footwork is really good down low and he seems to be able to get space for his shots so I don't see it being an issue in the post, especially because he can shoot so well with his left hand.