OBS actually uses the same codec as ShadowPlay if you have an Nvidia card (Nvidia NVENC), and also a general GPU based codec if you have AMD or don’t want to use the Nvidia codec (x264). Either way it runs really fast, barely any noticeable FPS drop. I have tested both encoders and they use up roughly the same resources. I haven’t tried comparing it to ShadowPlay yet, but I am pretty sure it will be the same performance wise.
No problem! 
On my old GTX 660 ti I was getting 70fps with no recording on in UE4, and 66-68 fps with OBS recording. I had used Fraps up until finding app so I was really amazed just how well it runs with UE4. I am certain you will get similar results with Day Z (and you can even overlay a webcam image of you playing it if you want! 
). With my new GTX 980 it is always maxed out at 120fps, it doesn’t affect the performance at all.
Just make sure to read the instructions, it is not overly obvious how to do the screen capturing at first… Quick Hint: You need to have a Scene first, so right click and add a new one in the Scenes box. Then right click in the Sources box to add a new capture source. You can create presets (or favorites) by creating multiple Scenes, each one has it’s own set of Sources.
No problem! Hope it works well for you!