Associating just with "javaw.exe" shouldn't work, because then the command is "javaw KoLmafia.jar" which tries to run class KoLmafia.jar, which doesn't exist.
The correct association is slightly more complex, because standard context menu won't have the correct option, as far as I have seen.
I think [1] the correct way is
Explorer (the one that opens with My Computer or when you "run" c:\, etc ...)
[menu] Tools
[menu item] Folder settings
[tab] File Types
find the row with JAR (or create new)
[button] more settings
select action "open"
[button] modify
set application: "C:\Program Files\Java\jre6\bin\javaw.exe" -jar "%1" %*
(point this to your javaw.exe)
Or you could use some sort of jarwrapper script to add that "-jar" instead. [2]
[1] I have localized windows, things may not be in exactly the same place or named as I "translated" them fro you
[2] I have actually taken to manually typing "java -jar KoLmafia<TAB><ENTER>" ...