169,080
Assuming the same rules apply to shampoo advertised/marked "For men" that do for deodorants, IE that they contain slightly higher concentrations of chemicals because men on average sweat more and perform more physical labour, those could possibly be ruled out.
Same for all the one "for women" with "super ultra moisturizing repair shine silky feel" splattered all over the labels, as those feel overdone. (In this case, I'd almost wager that shampoo for women are the really chemical-laden ones due to how men on average have shorter hair, but it's not like I've researched this or anything.)
That leaves the unisex generic ones, and the mild/sensitive/eco-friendly ones.
But really, anything *should* work. Takes a bit of experimenting is all.
At worst, you shouldn't have to go through more than four or five kinds.