No, we never found a real solution to get MuteX to work with skinning.
We switched over to using Atoms
Code:
#IFNDEF GlobalAddAtom
   External_Function GlobalAddAtom "GlobalAddAtomA" KERNEL32.DLL String sAtom Returns Integer
#ENDIF
#IFNDEF GlobalFindAtom
   External_Function GlobalFindAtom "GlobalFindAtomA" KERNEL32.DLL String sAtom Returns Integer
#ENDIF
#IFNDEF GlobalDeleteAtom
   External_Function GlobalDeleteAtom "GlobalDeleteAtom" KERNEL32.DLL Handle hAtom Returns Integer
#ENDIF

Function szGlobalAddAtom Global String sAtom Returns Integer
   Integer iAtom
   Append sAtom (Character(0))
   Move (GlobalAddAtom(sAtom)) to iAtom
   Move (iAtom iand |CI$FFFF) to iAtom
   Function_Return iAtom
End_Function

Function szGlobalFindAtom Global String sAtom Returns Integer
   Integer iAtom
   Append sAtom (Character(0))
   Move (GlobalFindAtom(sAtom)) to iAtom
   Move (iAtom iand |CI$FFFF) to iAtom
   Function_Return iAtom
End_Function

Function CreateUniqueAtom String sAtom Returns Boolean
   Integer hAtom
   Move (ToANSI(sAtom)) to sAtom
   Move (szGlobalFindAtom(sAtom)) to hAtom
   If (hAtom) Function_Return False
   Move (szGlobalAddAtom(sAtom)) to hAtom
   Function_Return True
End_Function

Function DeleteAtom Global String sAtom Returns Void_Type
   Integer hAtom
   Move (ToANSI(sAtom)) to sAtom
   Move (szGlobalFindAtom(sAtom)) to hAtom
   While (hAtom<>0)
      Move (GlobalDeleteAtom(hAtom)) to hAtom
      Move (szGlobalFindAtom(sAtom)) to hAtom
   End
End_Function
and that worked for us