You will be able to run either of them from within the SSD Windows 7 on the HDD. No need to do it at boot.
A "Clean" command deletes (marks as deleted) all partitions and files on a HDD and leaves the HDD as "unallocated space" when finished. It doesn't take long to finish.
A "Clean All" command does the same thing as "Clean", but will secure erase all partitions and files on the HDD to make sure that they are permanently deleted instead of just marking them as deleted as the "Clean" does. A "Clean All" can take a long time to finish running.
For what you described, I would recommend running the "Clean" command. "Clean All" is usually for when you are selling or giving the HDD to another person, and/or you wanted to make sure that nothing can be recovered from the HDD.
Hope this helps,