my $sp_str = "[\\s".chr(160)."]";
my $sp = qr/$sp_str/;

my $str = " ".chr(160)." ";
print "Happy\n" if $str =~ /^$sp*$/;
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Have a look at perldoc perlrecharclass (Perl Regular Expression Character Classes). If your string is in UTF-8 format, then \s will match all of:

 0x00009        CHARACTER TABULATION   h s
 0x0000a              LINE FEED (LF)    vs
 0x0000b             LINE TABULATION    v
 0x0000c              FORM FEED (FF)    vs
 0x0000d        CARRIAGE RETURN (CR)    vs
 0x00020                       SPACE   h s
 0x00085             NEXT LINE (NEL)    vs
 0x000a0              NO-BREAK SPACE   h s
 0x01680            OGHAM SPACE MARK   h s
 0x0180e   MONGOLIAN VOWEL SEPARATOR   h s
 0x02000                     EN QUAD   h s
 0x02001                     EM QUAD   h s
 0x02002                    EN SPACE   h s
 0x02003                    EM SPACE   h s
 0x02004          THREE-PER-EM SPACE   h s
 0x02005           FOUR-PER-EM SPACE   h s
 0x02006            SIX-PER-EM SPACE   h s
 0x02007                FIGURE SPACE   h s
 0x02008           PUNCTUATION SPACE   h s
 0x02009                  THIN SPACE   h s
 0x0200a                  HAIR SPACE   h s
 0x02028              LINE SEPARATOR    vs
 0x02029         PARAGRAPH SEPARATOR    vs
 0x0202f       NARROW NO-BREAK SPACE   h s
 0x0205f   MEDIUM MATHEMATICAL SPACE   h s
 0x03000           IDEOGRAPHIC SPACE   h s
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CountZero

A program should be light and agile, its subroutines connected like a string of pearls. The spirit and intent of the program should be retained throughout. There should be neither too little or too much, neither needless loops nor useless variables, neither lack of structure nor overwhelming rigidity." - The Tao of Programming, 4.1 - Geoffrey James

$ perl-5.14.2 -wE 'say "\xA0" =~ /\s/'
1
$ perl-5.14.2 -wle 'print "\xA0" =~ /\s/u'
1
$ perl-5.12.2 -wE 'say "\xA0" =~ /\s/'

$
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$ perl -wle '$_ = chr 0xA0; utf8::upgrade($_); print /\s/'
1
$
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\s is suppose to match U+00A0 and sometimes does. It's a bug in Perl that cannot be fixed for backwards compatibility reasons. You can indicate you want the fix using feature unicode_strings. In earlier versions of Perl, you can also work around the bug by upgrading the string's internal format.

use strict;
use warnings;
use feature qw( say );

my $string = chr(160);

no feature qw( unicode_strings );
say $string =~ /^\s*$/ ? 1 : 0 ;     # 0

use feature qw( unicode_strings );
say $string =~ /^\s*$/ ? 1 : 0;      # 1

no feature qw( unicode_strings );
utf8::upgrade($string);
say $string =~ /^\s*$/ ? 1 : 0;      # 1
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Note that the feature unicode_strings was introduced in 5.12, but to make \s match \xA0 on a non-utf-8 strings, you need 5.14:

$ perl-5.14.2 -wE '$_ = chr 0xA0; say /\s/ || 0'
1
$ perl-5.12.2 -wE '$_ = chr 0xA0; say /\s/ || 0'
0
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The -E enables "use feature 'unicode_strings'".