Thanks a lot for this suggestion! In my case the required version of the installer was not present in this location. But it helped me to find a solution!
Here are the steps I've taken when the required installer (for the currently installed version of the Evernote) for unclear reason was missing and that was not allowing new version of installer to uninstall the existing version of the application:
Go to the "C:\Users\Your Folder\AppData\Local\Evernote\Evernote\AutoUpdate" folder
Find/open "current.xml" file and copy the URL of the current Evernote version installer
If the "current.xml" for any reason is not present - check if there is an "update.xml" - URL of the installer of the Update version could be copied from here, but to download the current version you will need to change version number of the installer in the URL to the one you can find from the Evernote->Help->About menu.
Final URL in this case will looks like: http://cdn1.evernote.com/win5/public/Evernote_<your-CURRENT-evernote-version>.exe,
for example: http://cdn1.evernote.com/win5/public/Evernote_5.9.9.9915.exe if "5.9.9.9915" is a Currently installed version.
Paste copied URL into Browser address line and download missing installer to local drive
Run the downloaded installer and it will "refresh" current version of Evernote
After that you can check for updates and install newer version of the application
Thanks once more for your help!