Keep reading through the file, a block at a time, until you get to the block with your character. Print out the block up to your character, then whatever you need to insert, then the rest of the block. Then just loop until EOF, again a block at a time, for the rest of the file.

Something like this:

#!/usr/bin/perl -w

use strict;

my($replacepos,$replacestr)=@ARGV;

my $BLOCKSIZE = 10;
my $buf;
my $pos = 0;
while (read(STDIN,$buf,$BLOCKSIZE))
{
  # Does this contain our byte?
  if ( ($replacepos >= $pos) && ($replacepos < ($pos + length($buf))))
  {
    print substr($buf,0,$replacepos-$pos), 
      $replacestr, 
      substr($buf,$replacepos-$pos+1);
  }
  else
  {
    print $buf;
  }
  $pos += length($buf);
}
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10 is a good blocksize for demonstration, because it's easy to verify the edge cases. In real life, on most system 4096 is the best block size (it matches up with the size the system really reads from the disk).

If it's a genuinely tremendous file and there are actually performance problems, using Mmap might be more efficient (it is in C, I haven't use it in Perl).