Here's an example using Mojo::DOM, to make life easy, even with borked HTML. It replaces hrefs beginning with the selector ;widget=460, replacing them with the URL for this site.

#!/usr/bin/perl
use strict;
use warnings;
use Mojo::DOM;
use feature 'say';

# slurp from file, get from a live site via Mojolicious::UserAgent etc
+...
# hardcoded for example purposes

my $html = '<p><a href="https://example.com">example.com</a></p><p><a 
+href=";widget=460" rel="noopener" target="_blank"><img alt="Advertise
+r" class="banner" height="60" src="/images/articles/newsletters/Paper
+-v4-468x60.jpg" style="display: block; margin-left: auto; margin-righ
+t: auto;" width="468" /></a></p>';

my $dom = Mojo::DOM->new( $html );

for my $url ( $dom->find('a[href^=";widget=460"]')->each ){
    $url->attr('href' => 'https://perlmonks.org');
}

say $dom->content;
[download]

Output:

<p><a href="https://example/com">example.com</a></p><p><a href="https:
+//perlmonks.org" rel="noopener" target="_blank"><img alt="Advertiser"
+ class="banner" height="60" src="/images/articles/newsletters/Paper-v
+4-468x60.jpg" style="display: block; margin-left: auto; margin-right:
+ auto;" width="468"></a></p
[download]

Armed with this, it'd be trivial to have a list of widgets & their real urls, substitute the selector and static url value in the code above, looping through the list of widgets.

Update: See also Re: Batch remove URLs, or super search for more examples.