The obvious answer is that there’s nothing stopping you from running two browsers. Install Chrome or Firefox and you can access the modern web as well as your legacy systems.
http://portableapps.com/apps/internet/firefox_portable
http://portableapps.com/apps/internet/google_chrome_portable
Obviously the usual caveats apply to software from 3rd party sources, but portableapps.com has been going for years with no complaints.