Update:August 24 2015
In the old part of Dubrovnik there is a store at Đorđičeva 4 called Foto Felix. He has an assortment of accessories like SD cards and universal chargers. I also saw he had gopros. I bought an universal charger from him (400 kuna) with an adapter for lp-e6. He has to make some money right?
All other locations mentioned on Trip Advisor are closed or far from inside the city walls.
According to a question at Trip Advisor there is a place called HG Spot. Though I don't know the language very well I was able to see that they have a lot of stuff in the webshop that would suggest they would also sell the chargers.
Dubrovnik, Put od svetog Mihajla 37b
Tel. +385 20 420 565
If you are staying at a hostel or nicer hotel they might allow you to use that as delivery address and you can shop through any web store. They might also know a shop for you anyway and can arrange for transport there. This kind of knowledge is best left to the locals in my experience, when the stores close the websites are usually the last place to update.