It would be an interesting project to write a wee DNS server with a safe net back end. The back end would do the lookup against safe net to resolve the IP address, then allow the browser to connect with the clear net site directly.
The safe net back end could adopt a simple convention, by leaning on safe net DNS. Literally, you could register the exact domain on safe net, and upload an ipv4.txt file to the route, which would just contain the IPv4 IP address (IPv6.txt could service ipv6).
The DNS server could run locally, along with the launcher. It would listen on port 53 like a normal DNS server, but it would request the safe ipv4.txt file (e.g. safe://maidsafe.net/ipv4.txt), which would return the IP address. Anything that was not found could just proxy to a regular clear net DNS server instead.
There are open source clear net DNS servers, which could be patched to do this relatively easily. It could be fast too, especially with some caching.
Finally, the alpha network could do this reliably right now. Sure, it may get reset and it isn’t fully distributed yet, but it could work rather well.
Edit: You could also subscribe to DNS curators, who had a single safe net DNS url and resolved via url paths. This would circumvent safe net DNS, allowing an alternative (override?) mechanism if desirable.