How would that stop anything? Only "advantage" using a Linux Live CD in this context is that it will not leave any trace of the surfing history.
A live CD will also acquire no malware - a virus vanishes when the surfing history does.
My Vigor 2100 router has the ability to deny web based requests for ActiveX, Executable files, Mulimedia files, Cookies, Java, Proxies etc as well as key word denial and accepting IP subnet ranges.
That's what the HTTP CONNECT method (secure https:// pages) is for: to keep a router from sniffing for malware.
Well... You could install VMware and then install a linux guest. You could surf away with impunity on the guest with no risk to the host machine. Maybe a little more work than its worth though.
This is my approach to security now except that I use
VirtualBox instead of VMware (VirtualBox is free for noncommercial users).
In addition to malware this also helps prevent "barnacles": various software like drivers, plugins, utilities, updates, etc, that you maybe tried out, or maybe got downloaded by some program anyway. My host system only has four programs installed - VirtualBox, SpeedFan, PuTTY and TightVNC - and about 20 VMs where the action is. Internet Explorer is disabled in the host.
Unfortunately you need a high degree of nerdhood in your soul for this to be practical.