It is best to have a hair transplant. If this is not possible, then you should remove the wig every time you want to pray. If this is not possible, you should make tayammum every time you make ghusul.
As for only wudhu, wiping over this wig is sufficient.

I’m a 25 year old man and I have lost all my hair. This makes me look ugly and aged as per today’s society. I want to know the permissibility of non-surgical hair transplant where they use hair from other men and make it a wig like structure and then infuse/stick it to your scalp. However you still feel the scalp and hair. Also would wudoo be valid on this?