Two ways come to mind. First, like Juerd's, use an assertion (lookbehind in this example):

    my $delete  = join '','a'..'z'; # remove all lower case letters
    my $exclude = 'aeiou';          # exluding vowels

    $_ = 'Just Another Perl Hacker';
    s/(?:[$delete](?<![$exclude]))+//g;
    print;
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Or, slightly more complex, remove the exclusion characters from the deletion set first. This should prove more efficient, especially if you are repeatedly applying the deletion regex after you create it:

    my $delete  = join '','a'..'z'; # remove all lower case letters
    my $exclude = 'aeiou';
    $delete =~ s/[$exclude]+//g;    # excluding vowels

    $_ = 'Just Another Perl Hacker';
    s/[$delete]+//g;
    print;
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Either way, it is relatively simple to add or remove characters from your exclusion set.

Update: By "slightly more complex" I mean that it entails an extra step on your part --- in truth, I think it is the logically simpler version.