Before you start, you'll need GCFScape [web.archive.org] and VTFEdit [web.archive.org]. Pretty standard stuff for messing with Source modifications.

If you already know how to use GCFScape to remove sounds and stuff, skip to step 5.

1. Subscribe to +Ultra Particle: Texture files and run the game once.
   
2. Open your L4D2 local files and open the "addons" folder, then the "workshop" folder inside it.
   
3. Find 2778742681.vpk - this is the file containing the textures for +Ultra Particle Effects.
   
4. Open 2778742681.vpk with GCFScape and extract all the files to your folder of choice. Give it a name, such as "blur b gone".
   
5. Open the "materials" folder and then the "particle" folder.
   
6. Open the following files with VTFEdit and add the parameter $no_draw 1 to them. The location doesn't seem to matter, just put it in a line above a closing bracket. ( } ) Don't forget to save once you're done.
   - beam_distort_1.vmt
   - beam_distort_2.vmt
   - beam_distort_3.vmt
   - beam_distort_4.vmt
   - beam_melee_add_usez.vmt
   - beam_melee_add1.vmt
   - beam_melee_trans1.vmt
   - beam_melee_transadd1.vmt
   - beam_trail_tf2.vmt
   - beam_trail_tf2_ob.vmt
   - beam_trail_tf2_usez.vmt
   - particle_meleeblur_noz2.vmt
   - particle_meleeblur_nozadd.vmt
   
7. Go back to the main directory in your L4D2 local files. Open the "bin" folder.
   
8. Find vpk.exe. Drag and drop "blur b gone" (or whatever you called the folder) onto it.
   
9. Go back to the location of the folder and you will find a .vpk with the same name. Move it to the "addons" folder to make the game load it.
   
10. Unsubscribe from +Ultra Particle: Texture files on the workshop.

If you did everything right, all the blur and distortion added to melee weapons by +Ultra Particle Effect should be gone. Hopefully this will be helpful to fellow motion blur haters.

Slight disclaimer: I took a bit of a brute force approach during the making of this guide, adding $no_draw 1 to anything that looked like it was related to melee blur effects. I don't have the time to test nodraw on every single file individually, and I have no idea what the _tf2 files do. Sorry.