Hannah, one thing you might try is to use the non-zipped form of the updater. If you click the following link you will get the .exe version of the installer, so there’s no need to unzip it.
Download that one, and give it a try, and see if it helps your issue any.
Another thing to try would be to download the above .exe version, and then move it to a different folder (out of your Downloads folder) – say to the root of your C:\ drive. Then try running it from there to do the update.
Now, it may be that none of these suggestions fix the problem with the updater not finding your AxiDraw. But they are good first steps before we get into more involved debugging.