My husband is taller than average and consequentially, has longer arms than average as well. He's had a few dress shirts with long sleeves that he never wears because the sleeves are too short. So I've made them into short sleeves for him so he can wear them.
Here are my instructions for making a man's long sleeve dress shirt into a short sleeve dress shirt.
First, measure an existing short sleeve dress shirt to know how long to make the sleeves.
On mine, the top measured about 10.5".
With a couple of the shirts, I did struggle a bit where the sleeve width changed a lot just in that 1.5" of hem. The hem would bunch a bit near the seam, but I went ahead and sewed it and they turned out alright. Unless people look closely, I don't think they'll notice.