If you can be reasonably sure that your header will only appear once in your input file, then the following approach can work:

my $header = <>;
while (<>) {
    # process each subsequent record
};
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If you are really reading from <> instead of manually looping over the files, you cannot be reasonably sure that the header line will not occur again in your input stream as likely each file has its own header line. Then you can check $ARGV to see if the current input file has changed I think, and discard the first header line again.

This approach will of course only work if no header lines come in the middle of your input streamv as is likely when multiple files are concatenated together...