I'm due to build my first computer tomorrow, however I am a little concerned about how I will go about discharging static electricity due to the parts I have chosen.
I am using the Fractal Design Core 1000 case and the Corsair Builder Series CX 430W V2 PSU.
After doing my research I've found that the best way of discharging the static is electricity is to plug in the PSU and then touch a non metallic part of the case. The problem is that on my build both the case and the psu look to be both completely painted, with no metallic metal showing.
Will this be a problem or is there another method I should use?
No - do not plug in the power supply before building. Instead all you have to do is just build on a clean surface and you will be fine. Use a plastic floor mat if you're worried about conducting static while building.
Actually to ground yourself you should touch something metal that is grounded. The screw on a wall power outlet faceplate works fine. Touch it for a moment to release any static your body has built up. Then don't drag your feet across the carpet etc. and you will be fine. Normally the paint is not sufficient to prevent you from being grounded.
I have used the method you are referring to. Because a power cord is 3 pronged that means it is grounded and the metal on the psu is also grounded. Touching the metal case is enough to ground you if it is plugged in (no need to turn it on)
If you buy a wrist strap they often just have you attach the wire to the faceplate on the power outlet like I said in the first para. Since you can ground yourself so easily they aren't even worth the $5 they charge.