Alternatively, You could actually put a URL into $url. You won't have that problem since URLs can't have spaces.

use URI::file;
my $path = 'C:/Code/Perl/Phi Kap/temp.html';
my $url = URI::file->new($path)->as_string();
system "start $url";
[download]

Update: Nevermind, this doesn't work. start recognizes the http URI scheme, but not file one (because the HKEY_CLASSES_ROOT\file doesn't have shell\open defined).