Technically, the F# key(cup) is the one located above the key you close to play F natural. The key you press to finger regular F# is called the E key. If you mean the key above the one you press to play F natural is wobbly, then that indicates a problem greater than key noise. This key is crucial to the most important area of regulation of the sax and must have no side to side or back and forth play in order to work properly.
Now, to answer the question. The quick and dirty solution is to swedge both ends of the key while it is on the instrument using swedging pliers if possible. The better solution is to remove the key, over swedge the ends of the hinge tube (I prefer to use a collet tool), face the ends of the hinge tube and posts, and replace the key. This is a regular procedure done to every key on the saxophone when doing a thorough and detailed mechanical overhaul, and takes a great deal of time when done precisely.