My solution was to find an old 2-button mouse and plug it in.
I tried all the answers I saw above. Most seem to ignore part of the problem, which is that mac keyboards do not have alt or the windows key, in addition to the mouse not having two or more buttons.
I also did not understand what they expected the cursor/mouse to be doing while you hit shift-f10 or whatever. I want to lock an icon to the launcher, there is no way to select it first and then hit some key sequence. I can hover over it, or I can left-click it. Left-click and hold, then key sequnce while holding? Doesn't seem to work.
The answer above with xmodmap and xev commands seems like it might point in the right direction. But It's more like a "the solution exists" rather than an actual solution. Which key can I remap without messing things up? Shift-f10 seems to do nothing now, how would I use xmodmap to map menu to shift-f10? At least it provides a place to start the web search.
Also, the menu that comes up when I invoke "xdotool key menu" while hovering the mouse over something is not the same menu that comes up when I right-click on the same item. So "menu" is not quite what the OP asked for.