Presume you will be using this pickguard?
Doesn't do much around neck pocket area as it looks like there are black pickup mounting rings.
From those shots it doesn't look too bad, just a wee bit tight and sanding either sides should be all you need to do. If it required a few mm widening that is where a chisel comes in handy. Wrapping sandpaper around a rectangular shaped pencil eraser may help to keep things square.
Still reckon you need to temporarily install bridge as mentioned before and also install the high & low E tuners so you can run some cotton or fishing line over the nut and down to bridge saddles. This helps to see how parallel everything is and whether neck is sitting too far to one side or the other. Very handy to know so that you don't sand too much on one particular side when the other may need more attention. This also helps with locating the 'Centreline' of the guitar too.