The North is a different place than the South. The custom of the Hand is a Southern thing. Northerners do something themselves or don't do it at all. Eddard taught this to his kids. When he executed the deserter from the wall himself rather than let an executioner do it for him. There is even a line he says afterwards (that I can't remember now) about not being like the Southerners.
The Hand is used as the Kings second, so the King is free to go hunting, whoring, or doing whatever else that is not as boring as running a country.
So to answer your question, no he didn't have a Hand nor did he wait to appoint one.