I Highly Doubt that any Intel Card will run it. Sorry
I remember My Old HD3200 Could barely Play Fallout 3. And a HD3200 Was better than all Intel cards at that time. so if this is a new Intel Card and a 6310M can probably be barely enough to play it. then a Intel Card won't.
Sorry, Get a New GPU or Get it on Consoles. I wouldn't risk buying it and it not working.
But Remember thats my Personal Opinion Maybe someone with more Intel Integrated GPU Knowledge Could help out.
You can probably play Skyrim with an Intel HD 3000 graphics core with a mix of low and medium settings (mostly low though).
I have a Lenovo IdeaPad Y470 with a 1366x768 resolution screen. It has a GeForce 550m graphics card, but it can be switched off so that Intel's solution can be used. The HD 3000 can play Fallout 3 with decent enough performance with a mix of low & medium settings. However, you need to download the d3d9.dll developed for "Oldblivion" in order to be able to trick Fallout 3 to think that you have a discreet graphics card instead of integrate graphics. Fallout 3 simply does not recognize integrated graphics.
Crysis was playable at low settings using the Intel HD 3000. On average frames rate ranged between 18 - 24 FPS, but has dipped to around 11 frames sometimes in close combat. Overall playable, but just barely.
Mass Effects 2. This game is more demanding than Fallout 3, but less demanding than Crysis. However, gameplay stutters quite a bit in this 3rd person game. Enough that I decided not continue testing. I decided to end it after the 1st fight on Eden with those levitating armed probes (or whatever they are). ME2 is simply not playable at any level of enjoyment.
A word of warning, Skyrim uses the newly developed Creation Engine; Bethesda's own custom built engine. There is no way to gauge well that engine will perform in a relatively low spec PC since no other game uses Creation. On the plus side, Skyrim is developed for consoles as well, so it is possible a low spec PC can play the game.