If using the baby wash is working, I'd continue using it. I don't think that there is any reason to have to consider changing it until he's old enough that he wants to use what you are using. At 4, having a tearless shampoo is still a help.
I think my daughter switched when she'd used up all the baby stuff. She still buys products aimed at kids, tho. My granddaughter is 10 and she likes to use what Mama uses. I only have my own soap bar and shampoo here and they (her brother is 7) use that. I think I also quit using the baby wash when the bottle was empty and the kids were around 4, perhaps 5.