You could move the meat of the while loop to another place, like so:

sub some_function {
  # do stuff with $_
}

my ($word1, $word2) = split /\s+/,<>;
&some_function;            # $_ is the first line
&some_function while (<>); # $_ cycles through rest of file
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...and if you dislike egregiously abusing $_, you can throw in explicit variables in some_function.