After days of pondering I've just solved it myself, so I guess this becomes more of an FYI for anyone searching for an answer to this on Google like I was.

I had created the "hypdb" database having logged in using Windows Authentication so therefore with my Windows log in.

I deleted "hypdb" and disconnected from the SQL server, then reconnected again but logged in as "hypuser".

Then created the "hypdb" database again logged in as "hypuser", re-ran the Hyperion Configuration Utlity and was successful.

Appears as though you have to be the database owner to drop tables within it.