The vanilla sandbox will work for levels made to play on wars, but there is a seperate Wars editor. You download it as a part of the CrysisWarsModSDK_Tools package. If you have wars installed when you install that package it will install the wars editor for you.
To start it, you do exactly the same as you do for vanilla sandbox editor, substituting "\Crysis Wars\" into the path inplace of "\Crysis\" in your shortcut, adding "-mod MWLL" to the shortcut target field
To work on maps for wars, using the vanilla editor, you can move the MWLL folder from your wars install over to vanilla install, swap DLL's from bin32crysis into bin32 and start the editor to work on maps if you cannot download/access the wars editor. Then move the MWLL folder back, swap mwll.dll from bin32wars into bin32 and test your level in wars like normal(substitute bin64 etc if using 64bit versions).
There is also a slight issue at the moment where the community Beta has a slightly out of date "mwll_assets.xml" prefab library. This library is missing repair bay prefabs and a has an older mechhanger prefab that doesnt include the new solids that address the falling through hanger bug. We will fix this in a future patch, and get the community an up-to-date prefab library.