Baby Dandruff

My boy has had quite bad dandruff his whole life! The cradle cap wasn’t so bad, but he’s always had a dry flakey scalp. It doesn’t seem to be bothering him, but to me looks awfully dry and itchy! From a small baby because of this I’ve never used shampoo, only conditioner… and the last few months have only washed his hair once a week. But it’s still no better at all. Am I doing wrong by not using shampoo? Could that actually help? I’ve tried the cradle cap style oils when he was much smaller, but he hates it and I feel like I’d need to do it daily to help… I also use a spray in baby ‘Coco’ leave in conditioner once a week. Do I try alternative products? Or go no products at all?