Regexp::Common has a mechanism that simplifies this greatly.

#! /usr/bin/perl

use strict ;
use warnings ;
$|++ ;

use Regexp::Common qw( delimited ) ;

my $str = do { local $/; <DATA> } ;

print "\nBefore\n-----\n", $str ;

$str =~ s/$RE{delimited}{-delim=>'"'}{-keep}/'$3'/gs ;

print "\nAfter\n-----\n", $str ;

exit ;

__DATA__
  "Welcome to my humble abode," I said, spreading my arms.
  "You mean, you live here?  In the monastery?"
  "Absolutely.  Come, I'll show you about.  Everything you need
is located right here, from tutorials to friendly advice."
[download]

Those who know that they are profound strive for clarity. Those who
would like to seem profound to the crowd strive for obscurity.
            --Friedrich Nietzsche

It might be worth pointing out that, given yout trivial example, $str contains identical information regardless of which form of quotes are used.

That is to say

$str1 = "Some String";
$str2 = 'Some String';
if( $str1 eq $str2 ) { 
    print ">>$str1<< is identical to >>$str2<<\n"; 
}
[download]

Gives:

>>Some String<< is identical to >>Some String<<

So, without resorting to something esoteric like source filtering, the only way to change the quotes (in your example), is to do so manually with your editor!

So changing how the strings are quoted only becomes meaningful if the strings you are programmically changing contain embedded quotes. eg.

$str1 = "'Some String'"; 
$str2 = '"Some String"';
if( $str1 ne $str2 ) { 
    print ">>$str1<< is different to >>$str2<<\n";
}
...
>>'Some String' is different to >>"Some String"<<
[download]

Therefore, your question only really makes sense if the source of the contents of the strings is external to your program as DamnDirtyApe demonstrated.

Is this what you meant?

while (<>) {
    tr/\"/\'/;
    print;
}
[download]

I would not recommend using this approach on a text file that contains a perl script. Consider what would happen with a code snippet like the following:

$name = "my name";
print "---$/ What is $name ? \t I won't tell.\n---";
[download]

---
 What is my name ?         I won't tell.
---
[download]

---$/ What is $name ? \t I won't tell.\n---
[download]

Single quotes in perl scripts are used to assign literal string values, without interpolating variables or special characters like \n, \t, etc.