$ perl -MHTML::Entities -e'print encode_entities(q(I have a 15" latter and a 6" foot arm.))'
I have a 15" latter and a 6" foot arm.$ 

##</code><code>##

use HTML::Entities;
my $str = q("I have a 15" latter and a 6" foot arm.");

my $re = qr/^("?)(.*?)("?)$/s;
$str =~ s/$re/$1.encode_entities($2).$3/e;

print $str, $/;

__END__
"I have a 15&quot; latter and a 6&quot; foot arm."

##</code><code>##

use HTML::Entities;
my $str = q("I have a 15" latter and a 6" foot arm.");
substr($str, 1, -1) = encode_entities substr($str, 1, -1), q(");
print $str, $/;
__END__
"I have a 15&quot; latter and a 6&quot; foot arm."