Why not create a copy of the string with the special char removed and use that for the initial matching?

Alternatively you could:

use strict;
use warnings;

my $matchStr = 'aabb';
my $match = "\xff?" . join ("\xff?", split '', $matchStr) . "\xff?";
my $str = "aa\xffbb";

if ($str =~ $match) {
    print "Matched";
} else {
    print "No match";
}
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