You can open each file separately in a simple foreach loop:

foreach my $file (@ARGV) {
    open my $fh, $file or warn("Cannot open file $file: $!\n"), next;
    my $header = <$fh>;
    #process header
    while (<$fh>) {
        # process file
    }
}
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It is generally more reliable and controllable process than using <>. Reading the first line with smth like my $header = <$fh>; was already described in the above comments.