I don't think his problem is ball-handling really. He doesn't have a great handle relative to other guards, but he's good enough to make straight two-bounce drives to the hoop.
His problems IMO are that he isn't good in the paint when he does get there - he's a mediocre finisher and he doesn't have the mindset to draw fouls and get to the line. I don't remember the last time I saw him go up and challenge somebody at the rim, but I know for a fact that he has the athleticism to do it.
He uses his dribble to move laterally for an open midrange jumpshot, and he makes them at a good (though streaky) clip. That's a double-edged sword - he's a good shooter in that range, but the midrange jumper is an inefficient shot by nature and it reinforces the notion that he doesn't have to attack.
That's why he has lines like 19 points on 9-16 shooting - despite having a great game from the field, it's still not very efficient because he doesn't take a lot of threes and he rarely gets to the line. So his next step has to be one of those two areas - either start attacking and drawing fouls, or improve that three point stroke and start launching from beyond the arc.