I attempted a playthrough of Red Dead Redemption knife only (well mostly). I was allowed to use throwable items when absolutely necessary, but everything was done without guns. No skipping missions and no glitches. Enjoy!
GTA V No Wanted Stars challenge:    • Can You Beat GTA V With No Wanted Stars?  
TLOU pistol only run here:    • Can You Beat The Last of Us Part I Pi...  
Uncharted 2 melee only challenge:    • Can You Beat Uncharted 2 Without Guns?  

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Songs Used:
Western Spaghetti Chris Haugen
Way Out West Chris Haugen
Way Out West Twin Musicom
Drankin Song Kevin McLeod
Country Boy Benjamin Tissot (Bensound.com)
Badass Benjamin Tissot (Bensound.com)

Chapters:
0:00 Intro
0:23 Rules
0:43 New Austin Chapter
10:50 Nuevo Paraiso Chapter
20:40 West Elizabeth Chapter
27:08 Marston Ranch Chapter
30:07 Summary