Kaspersky seems to be storing windows update files on the C Drive:
Here -> C:\ProgramData\KasperskyLab\adminkit\1093\.working
Change folder location with klsrvswch.exe utility.
You can reach it from the KSC installation folder. Utility named as "Administration Server Account Switch Utility". It seems like just allows you to switch service account, but also allows to change "wsus" folder path. Continue wizard as if you want to switch service account. You don't need to provide a new service account, you can use current. Last step is the place of path change.
