You can't do that with pure ip-routing. For that you have to use policy-basrd-routing:
First you have to specify the traffic that should be routed in a specific way:
ip access-list extended WEB-TRAFFIC
permit tcp any any eq 80
permit tcp any any eq 443
Then specify the routing in a route-map:
route-map WEB-POLICY permit 10
match ip address WEB-TRAFFIC
set ip next-hop 44.44.44.44
Last, apply the route-map to the interface where the WEB-clients are located:
int vlan X
description LAN-interface
ip policy route-map WEB-POLICY
Here are some links to more information on PBR:
http://blog.alwaysthenetwork.com/tutorials/policy-based-routing-tutorial/
http://www.petri.co.il/how-to-use-cisco-ios-policy-based-routing-features.htm