The best approach: You do not.
Lockpicking is less than worthless. There is basically nothing that you can't unlock with a key or just by breaking things open. There is no good reason to take Lockpicking on any character.
While you can solve the mystery through pickpocketing, you can also solve it by rummaging through containers near the suspects to get similar items.
There is a Scoundrel companion
In the well just west of Cyseal's west gate
, who would make a good fit for the things you want a Scoundrel for.
No trailing s in the spoilers tag, by the way.
