You will want to run an elevated Azure role startup task (see http://blogs.msdn.com/b/avkashchauhan/archive/2011/03/17/using-startup-task-in-windows-azure-detailed-summary.aspx) and run the following command to remove ClientIP field from logs:
%windir%\system32\inetsrv\appcmd set config -section:sites -siteDefaults.logfile.logExtFileFlags:Date,Time,UserName,ServerIP,Method,UriStem,UriQuery,TimeTaken,HttpStatus,Win32Status,ServerPort,UserAgent,HttpSubStatus,Referer
In the above command line "ClientIp" is removed which should remove the user IP field from the logs.