...may contain 1 or more of the characters smtwhfa in any order.

That means you want '+' instead of '*' for the quantifier.

You can make sure there are no repetitions with a hash over the characters:

if ( $string =~ /^[smtwhfa]+$/
    and length $string == do {
        my %hsh;
        @hsh{split //, $string} = ();
        keys %hsh;
    } ) {
   # everything's ok
}
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That uses the uniqueness of hash keys to enforce your requirement.

You can do that with regex lookahead by a negated match, $string !~ /([smtwhfa])(?=.*\1)/ after the match for the character class. That returns true if there is no match for a repeated character (untested).