Your question about whether it is possible to add shortcuts to the desktop using the Arc menu has been on my mind since you have asked this question, as it also bothers me when I have to make the Zorin menu visible for this purpose, which I don't normally use. Now I have found a solution for this:
Install the gnome extension "Desktop Icons NG (DING)" and make sure that it is enabled. Then the option "Create a desktop shortcut" (or to remove the desktop shortcut when there is already one) will also be displayed in the right-click menu.
After adding the desktop shortcut, right-click on the icon on the desktop and select "allow launching."