Rather than using captures and substituting with $1$2 I would probably use look-behind and look-ahead assertions so that I can substitute just my stop word with nothing.

use strict;
use warnings;

my @stopWords = qw{the on};
my $title =
   q{The% cat sat 4on5 the %tHe% hat %On};
print qq{Title   : $title\n};

foreach my $stopWord (@stopWords)
{
    print qq{Weeding : $stopWord\n};

    # Do substitution using extended regular
    # expression syntax to allow comments in
    # the pattern.
    #
    $title =~ s{(?x)   # Substitute ...
       (?:             # Alternation for look-behind
          (?<=\A)      # If preceded by string start
          |            # or
          (?<=[%0-9])  # percent or digit
       )               # Close alternation
       (?i:$stopWord)  # ... ignoring case, stop word ...
       (?=[%0-9]|\z)   # If followed by percent or
                       #   digit, or string end
       }{}g;           # ... with nothing globally

    print qq{Title   : $title\n};
}
[download]

The output is

Title   : The% cat sat 4on5 the %tHe% hat %On
Weeding : the
Title   : % cat sat 4on5 the %% hat %On
Weeding : on
Title   : % cat sat 45 the %% hat %
[download]

I hope this is of use.

Cheers,

JohnGG