I have used Win7 and Classic Shell for quite a while, but I had installed Classic Shell at roughly the same time that I first started using Win7, and I had also made the custom Desktop icon launch for Windows Explorer. I had made similar custom Windows Explorer launches for my previous versions of Windows, so when I just started using Win7 and also just started using Classic Shell, I had created this custom launch for Win7, I just took it for granted that it was a "bug" of Classic shell. I liked many of the other benefits Classic Shell so much that I felt that small inconvenience was well worth it.
I had roughly roughly looked in here at the forums from time to time to see if anyone else had made mention of it. I felt that the second launching might get mentioned at some point, but I never saw it, so that's the reason that I brought it up. In the previous versions of Windows, I had never had this happen before, so I naturally took it for granted it was Classic shell, and hoped for a future fix. When the more recent update happened and the second launching still continued to occur, I felt that I should mention it.
I am very surprised this was related to Microsoft, since I had never had this happen to me before, so I am big enough to step forward to admit my embarrassment and mistake. I hope this entire posting of my assumption will be of some benefit to some other person that might be suffering from the same issue, just lurking for an answer, and that they will read it and perform a similar fix.
Again, my apologies to the developer(s) of Classic Shell.