From the term "raw data" it appears that you have backup of partitions of old server like /home, /usr, /var etc. If this is the case then in order to restore the sites, you can simply create empty accounts with same Usernames. After that just copy the user folders under /home from old server's backup to new server's /home partition. Also copy the complete /var/lib/mysql contents from old to new server's /var/lib/mysql. Make sure the MySQL version on the new server is same as it was before on the old one.
As far as old server's WHM configurations are concerned, I believe it shouldn't be a problem and new server server can be configured in short span of time with few clicks. Most of the configurations related files are under /var/cpanel directory but make sure that you are absolutely sure about what you are going to do before you actually do it regarding copying any configuration related data.
Hope that will help.
