GAG is correct the key remapping is via registry entry and is global across all applications and users. Any changes require a restart.
However this hardly poses a problem greater than the benefit. The F1 key is used as "Help" on pretty much every program I run yet those same programs all have the little Blue Question Mark Icon in the tool bar which provides the same function, so you lose no functionality whatsoever.
Looking at my circumstances again I actually remappped F1 to F9, but left F9 as F9, this means no functioning F1 key. I've had it this way for several years now and not once have I ever needed the functionality of the F1 key. The fact that I can use this key as a shortcut in ArchiCAD FAR outways any minor inconveniance.