If you are running squid as a transparent proxy, add entries to your PREROUTING table that use "-j RETURN" before the the entry that does the REDIRECT or DNAT. For example
iptables -t nat -A PREROUTING -d www.linuxquestions.org -j RETURN
iptables -t nat -A PREROUTING -p tcp --dport 80 -j REDIRECT --to-ports 8080
would send LQ requests directly to the Internet, but redirect everything else to the proxy listening on 8080.
Alternatively, with either transparent or non-transparent proxy, I think you could use privoxy
as your first proxy. You can then run privoxy "disabled" (which means it won't make any modification to requests or web pages) but configure it so that it passes most requests on to quid
, but passes select URLs directly to the Internet.