There's alternative GUIs for editing the menu that you can try, for example MenuLibre. I assume, MenuLibre allows adjusting that freely, but I haven't actually tried it.
But yeah, as @[email protected] already pointed out, what these GUIs do, is just editing the .desktop file, which you can also edit with a text editor.
You probably already have a file for the application you're trying to correct underneath ~/.local/share/applications/. If you don't, then copy it to there from /usr/share/applications/.
And then find the [Desktop Entry] section and edit (or add) the value for Icon= to contain the absolute path to the image file you want to use.
Normally, the menu picks up such changes immediately, but if in doubt, you can try logging out and back in...