Yes it is possible to braid a non modular PSU, there are 3 ways to do it
1. Use braided extensions.
2. Braid the plug end of the cable as normal and described in this tutorial. The other end of the braid, shrink some heat shrink onto the wire directly, then place the braid over this and shrink some more over the top. This creates heat shrink braid sandwich which will hold the braid firmly in place. Note though while the braid will not come loose, the heat shrink might be able to move up and down the wire and therefore you will not be able to strecth the braid.
3. Braid the plug end of the cable as normal but the other end, open your psu and put the braid inside your psu. This will give you the neatest and most complete look however it is risky if you don't know what you are doing and will invalidate any warrenty you have.
Depending on your skill level with psu and what look you are going for the choice is yours.