My elderly father refuses to shower because he says it makes him itch. How should I handle this?

Once a week seems alright. Does he smell, does the place smell? If not, then let it be. If he is smelling, then look at the shower and see if any changes can be made to make it easier for him to shower. Take a look at his skin, is it breaking down. At 91 the skin is like thin paper and there is no fat underneath to insulate, so taking a shower in an unheated bathroom would be cold. Depending on your resources, putting a heater in the bathroom might help, but make sure you can control it and lock it, the heater control unsupervised is unsafe.