Instead of using Find (like ++poj suggested), you could also iterate thru all the Item()s in the Hyperlinks() collection. Instead of deleting each hyperlink and adding a new one, you could just edit the existing one. (If necessary, it would be easy to add in decision logic on each hyperlink.)

use warnings;
use strict;
use Win32::OLE;
use Data::Dumper;
    $Data::Dumper::Maxdepth = 2;

my $MSWord = Win32::OLE->new('Word.Application', 'Quit')
    or die $!;
$MSWord->{Visible} = 1;
my $doc = $MSWord->Documents->Open('C:/temp/hyper.docm');

local $, = "\t";
my $url = 'http://www.perlmonks.org/';
my $HLs = $doc->Hyperlinks();
foreach my $ihl ( 1 .. $HLs->Count ) {  # ->Item() is 1-based, not 0-b
+ased
    print STDERR $ihl, $HLs->Item($ihl), @{ $HLs->Item($ihl) }{'TextTo
+Display', 'Address', 'SubAddress'};
    @{ $HLs->Item($ihl) }{'Address', 'SubAddress'} = ($url, '');
    print STDERR $ihl, $HLs->Item($ihl), @{ $HLs->Item($ihl) }{'TextTo
+Display', 'Address', 'SubAddress'};
}
$doc->Save;
$doc->Close;
[download]

There may not be much on the web for how to do MS Word OLE thru perl, but since the OLE uses the same API as Word's embedded VBA, I just searched for "word vba search for hyperlink", where I found this stackoverflow answer, or "word vba edit hyperlinks", resulting in this answer, and looked at the MSDN documentation for the Hyperlinks collection and Hyperlink object