I have short (fat) fingers and I find it very difficult to play many cords correctly. This was one of the reasons that I gave up guitar back in my younger days. However, I started back up learning the guitar a few months back, and in the last 2 months I have made a lot of progress that I never thought I would be able to do. Bar cords, forget it. LOL, but open string cords I’m making a lot of progress just by blindly play them and by practicing them over and over again.
Even while watching TV I’ll pick up a guitar and just play without an amp just to get my fingers to memorize the shape of the cords. Also depending on the type of music you are playing, many rock songs use the power cords which most all of us can do, even the short finger ones. 😊.
Basically, don’t give up. There are thousands of songs, and melodies you can play without learning every cord out there.