In general, I typically remove the bark as I have heard it can impart and off flavor/taste.
For as little wood that we go through with these efficient smokers, I would recommend getting some good smoking wood from a quality supplier rather than what is available via the big box stores. From what I have read here most of the big box store wood is kiln dried and too dry in general for our smokers. If you have some that you want to use to get rid of, some have soaked and/or placed the wood in foil packets with holes poked in it.
Here are some suppliers that have compiled:
I bought an extra bag of the hickory dowels and cherry from Smokin-It when I bought my smoker. So I am pretty well set on the basic two that many use. The hickory from SI is the best that I have used and I have tried 4-5 different kinds with my previous smokers. I may try some fruit woods at some point too.
I have been splitting my dowels and my cherry as the pieces for the most part are pretty big and splitting tends to let them burn more evenly. In order to do a split of say hickory and Cherry and keep the weight in the 2-3 ounce range you almost have to split them.
Most of the chunks that you will get in the big box stores as well as the suppliers that I listed above will still need to be split.
I have heard that either or maybe both Fruita Wood and Maine Grilling Woods have what they call a CookShack or an electric smoker cut that they can do if you ask for it. I don't see this special cut listed on their site unless I am just missing it.
Hopefully this helps.