You really want Focus Sash as an option on this, having a second life on something as slow, frail and damn powerful as Azurill is massive.
Substitute seems like a great option, certainly far better than Rain Dance or Charm. Sub lets you prepare for predicted switches, and there is no shortage of Water immune and Normal immune Pokemon just waiting to get a free switch into Azu. Think Croagunk and most Ghosts.
You could mention the gimmicky Belly Drum set in OO, combined with TR it would be scary but extremely hard to set up.
Also maybe a mention of a EV/IV spread on a non TR team, since with Sash its usable outside TR.
There is a pretty great Azu analysis approved on LCF, its got a discussion on the merits of several moves not mentioned here (Iron Tail, Double-Edge) and a lot of depth in many sections, you may want to use parts of it or at least look over for ideas.
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