No, this is not possible, at least without screwing up the software a little bit. It all really has to do with locations and permissions, and not so much about how the software actually runs.
See, if you install a software for a single user, it generally gets placed in your user profile; in the AppData folder, or in other locations, in some cases. Because these user profile folders are only accessible to the one who owns them, other users cannot use the software within these folders.
If you install a software for all users, it gets put in the regular "Program Files" folders, located in the root of the C:\ drive- and any user on that computer that can access said C:\ drive can run the applications installed onto it, unless a user puts a lock onto those folders, which is unadvised, as the applications themselves often cannot bypass the locks put on their folders.
Because of this, the only way to actually change a software install from being accessible by all users into just one user is via moving the folder that the software is located in out of its original install location and into the appropriate user drive folder. This can cause permission errors and multitudes of other problems in application operation depending on the application. Due to the way MySQL operates, it would probably quite disrupt proper operation if said folder move was preformed.
I would advise that you re-install the software for just your profile rather than moving its folder and risking breaking the software.
For MySQL, It would probably be a good idea to restrain folder access to the MySQL folder for the user you don't want accessing it, as from my experience with the software, it installs into this all users profile anyways. If you restrain their access to the application's folder, then even if they see a shortcut to the application, they won't be able to access it. I Won't go about describing how one would restrain such access, as there are many ways of doing the such. The best method would probably be tweaking the security settings in the preferences window of the MySQL Folder, but i'll leave that up to you.
Depending on the what the other applications are and how they installed, it may be as easy as just restricting user access to the folders of which the applications are contained. Some of them could be easily hidden to the user(s) you don't want to access them, provided that there are no shortcuts or links to these folders on their profile. If they can't view hidden folders then this user won't even be able to know that the applications exist. This method isn't quite as secure, though.
It quite depends on the application, really. If you could give me a list of every application you want to be only single-user accessible, I could compile a sheet of information on how to preform such an action.
If you really need 0 possibility of access to these folders, then you may want to look into some extreme encryption measures, and I would suggest going to this stack exchange site for that.
Hope I was able to help! :)
Why don't you just remove the shortcut from the User's profile. You can also change the permission on the folder so they cannot even view the contents of it. You could also just reinstall the application. – Ramhound – 2013-11-14T18:26:56.337
Because I need to do this sooner than later, I will likely so something with permissions and shortcut removal and so on to address my immediate need. Reinstalling applications would be too painful for my setup. What I am looking for is really something like @Ben Franchuk except that he answered in the reverse direction. I figure the answer is no you can't because ... but I would like someone to write that answer with the proper reasons included. – demongolem – 2013-11-15T14:07:18.837