I suspect that URI::Escape is the right choice. Here's a bit of code to compare them:

my $url = 'http://www.myothersite.com/myotherwebapp2/foo.asp?param=1&p
+aram=3';

use CGI;
print "Using CGI Escape:\n";
my $esc_url = CGI::escapeHTML $url;

print "$url\nbecomes\n$esc_url\n\n";

use URI::Escape;
print "Using URI Escape:\n";
$esc_url = uri_escape($url);
print "$url\nbecomes\n$esc_url\n";
[download]

Output is:

Using CGI Escape:
http://www.myothersite.com/myotherwebapp2/foo.asp?param=1&param=3
becomes
http://www.myothersite.com/myotherwebapp2/foo.asp?param=1&param=3

Using URI Escape:
http://www.myothersite.com/myotherwebapp2/foo.asp?param=1&param=3
becomes
http%3A%2F%2Fwww.myothersite.com%2Fmyotherwebapp2%2Ffoo.asp%3Fparam%3D
+1%26param%3D3
[download]