Clear, and most other standard antidandruff shampoos
on the market, contain 1% zinc pyrithione, which is
very drying. One is Kao.

I am using Watson's Dandruff Shampoo with 1% zinc pyrithione,
and it dries my right hand so bad it has worsened
my eczema there to the point of contact dermatitis.

Others have 0.4 to 0.8 %, so these are less drying, but at
the same time less effective against dandruff.

Other dandruff shampoos containing Piroctone olamine, also
known as Octopirox, are less drying. An example is the Himalaya
brand.

Some shampoos contain climbazole, but this is not very effective
as an antidandruff agent (one is Feather brand, I think).

The most effective antifungal agents are ketoconazole, used
in Nizoral shampoo, and selenium sulfide, used in Selsun.
However, these tend to be even more drying, especially the
those stronger concentrations.