I just went through the same deal.
1) Install Wars.
2) Forget everything learned from installing Crysis, assume Wars 1.0 will work with Crysis 0.41 data copied over from Crysis folder, fail.
3) Update Wars to 1.5
4) Do #2 again except with Wars 1.5
5) Read a couple of forums
6) Try to start a multiplayer Wars game, finally get the CD Key prompt.
7) Enter Crysis key. THIS APPEARS TO SUCCEED, or at the very least there is no error thrown.

Do #6 again, but now it says the entered key is wrong.
9) Enter the Warhead key instead, see no error, finally connect to an MP Wars game.
10) Figure it's best to be safe, re-download entire MWLL 0.40 package.
11)

12) Play MWLL, I hope >_<