Thank you, sir. I do see what you describe and it works well. I apologize for not stating better that I am trying to create desktop links for .exe files that run using wine. (Because I come from the Windows world, I assumed that everyone would know what I was talking about.)
I right-click on the .exe file and use the option of "Make Link" and move that link to the desktop.

My question is how to change the icon of that link on the desktop. That is where I do not see options available when I right-click, etc.

And, really, one HD installation of Knoppix DVD would not show a "Make Link" option when I right-click on a file, whereas another HD install on a different HD using the same computer does show that option for any file that I right-click on. But that's a quirk that I don't care to worry about now.

Sorry for any confusion.