Unless it's homework, this might be simpler.

#!/usr/bin/perl

# http://perlmonks.org/?node_id=1215296

use strict;
use warnings;

while(<DATA>)
  {
  /^~/ and tr/_/+/;
  print;
  }

__DATA__
A line with an_underscore.
A line with_two_underscores.
~A line with an_underscore starting with a tilde.
~A line with_two_underscores starting with a tilde.
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