He only wants to get some practice - then let him have his practice and be done with him.
The trick comes with the hassle that you have to visit each chest two times (three times, if you count the moment you saw and ignored it while fighting), but the very last one, when you handily dismis him. (He will yell he didn't do nothing and you'll give him right - you don't always need to have a reason at hand to let an NPC go.) 
It might not be everyone's cup of tea to do it like that, but it is an easy solution to an annoying problem.
Costs you nothing but time! 
Having a locksmith along permanently will cost you - though she will be cheaper than keeping the burglar of course - not sure what his percentage actually is or if it's random.
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