That makes me want to write Test::Skip that wraps ok(), is(), like() and so on to avoid having to duplicate the test name.

Hmmm. Interesting thought. I think you could just get away with something like this:

sub skip_unless (&$$) {
    my ($test, $name, $tests_to_skip) = @_;
    local $Test::Builder::Level = $Test::Builder::Level+1;
    my $passed;
    my $ok = \&Test::Builder::ok;
    {
        no warnings;
        local *Test::Builder::ok = sub {
            $_[2] = $name unless defined $_[2];
            $ok->(@_);
        };
        use warnings;
        $passed = $test->();
    };
    skip "failed: $name", $tests_to_skip unless $passed;
    return $passed;
};
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allowing you to do things like:

skip_unless { ok $mech->is_html } 'Returns HTML', 3;
....
skip_unless { is $foo, $bar } 'foo == bar', 3;
...
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So you wouldn't have to have N different *_or_skip routines. Not sure whether this would deserve a module all of its own though...