(Am new to web programming, so apologies for any lack of rudimentary knowledge.)
My page allows a user to select a file that is then read clientside & displayed
Sadly, the only answer I can come up with will hog some extra bandwidth.
Firstly, use something like if (typeof FileReader !== "undefined"
or Modernizr to follow your normal flow for the browsers that DO support FileReader. Otherwise, POST the file via AJAX to some server-side script that echoes back the contents.
So for compliant browsers, you get to save yourself some bandwidth and for non-compliant browsers you have to take one for the team.
Another solution is to use "A FileReader polyfill for Internet Explore and Safari using Flash"
See: https://github.com/Jahdrien/FileReader