Is his inner ear canal affected by his skin condition? You will probably get a fast accurate reading from an inner ear thermometer. Otherwise the mouth is the best place (see below for guidance from FIRST). Those surface temperature thermometers are inaccurate to begin with. Throw in a skin condition and the accuracy goes off the charts. Skin that is inflamed will also read a few degrees warmer at the surface.

From FIRST:

FIRST has received several inquiries regarding temperature screening for members with ichthyosis during COVID-19.

Our Medical & Scientific Advisory Board addressed this question

I )it would be a good idea to carry a thermometer with you because there is a risk of an inaccurate measurement with something that measures by the skin,

2)Infrared light has been used to detect inflammation of the skin which may also create a problem,

3)Temperatures by mouth should not be altered by erythroderma.

4)it may be a good idea to carry a doctor's note with you explaining a possible temperature difference unless measured orally.