The dialog box was recently redesigned, but the functionality hasn't really changed. If you have an image in your clipboard, you can use Ctrl-G to bring up the Imgur dialog box and paste the image using your OS's paste-from-clipboard keyboard command (often Ctrl-V or Command-V). No need to use the mouse or the file manager.
If you already have an image hosted somewhere, you can also use Markdown to link to the URL:
Malabarba has a rather fine Stack Exchange mode for Emacs, but it does not seem to support image uploads just yet. Perhaps it could provide some relief to your hotkey anoyance when composing posts without images?