Skyrim should be playable. I configured the game to run on a friend's laptop which has a dual core i5-4200u and the Intel Hd 4400. The quad core i5-4590 is more powerful and it's Intel HD 4600 graphics core is also a bit more powerful. I got the game running pretty decently at 1600x900 resolution with a lot of tweaking.
It has been a little over 1 year since I did it, but with an edited SkyrimPref.ini file I believe the performance ranges between 30 FPS to 45 FPS with brief dips as low a 25 FPS and brief spikes up to 50 FPS. The SkyrimPref.ini file gives you more control to the graphic settings. For example, there is no way to disable shadows without editing the ini file and that one of the things I did to get decent performance at 1600x900 resolution. Graphic settings were mostly low with some medium. I am pretty sure I left texture quality at high because dropping down to medium made the game look like crap.
There were a lot of tweaks I made to the ini file that I cannot remember, but off the top of my head, I am pretty sure there were some settings for texture sizes which I probably reduced to 128 or 64. But I know I did install various mods to improve performance like using a reduced size texture mods that actually had very little visual impact. But I also install mods that made the game look better with very little performance impact, if any.
You are going to have to do some research and install some mods to squeeze out the best performance such as Googling how to edit the SkyrimPref.ini file.