Handedness. Should i concentrate upon?

My child is 3y 11m old.  He uses both his hands to do mostly everything but right hand for brushing and right leg for kicking ball. apart from these two, every other activity he uses his left and then right. some friend suggested that I keep small things at the centre while making him sit and ask him to pick those up. he has used his left hand in 95% of times. the problem is while making him write. he hates writing, plus this handedness issue. I don't do homework, but during online classes I have to make him do classwork while holding his hand. he cannot write on his own. since last three months I have been doing this with right hand. but today I tried left hand, to see if I'm going wrong. I saw his finger pressure is more in his left hand than right.Pencil grip is almost same. But precision of lines is better in right, one reason being practice.Which hand should I concentrate upon? i don't want to make him use wrong hand while doing school classwork.