Yes, you can find the icon for the program and edit it without messing anything up. Usually they're in /usr/share/icons. You can also add a custom icon to the icon theme you're using.
Alternatively, you can use another icon theme. Although Mint-X has a TON of icons compared to most distros, it can't compete with something like Numix, my personal favorite. https://github.com/numixproject/numix-icon-theme-circle