There is no such thing as a short-sleeved dress shirt. Let me repeat: there is no such thing as a short-sleeved dress shirt.
In a previous post I quoted Alan Flusser in the context of the interplay between the suit jacket, shirt collar and tie. There are other areas in men's clothing where similar interesing elemental interactions are more visible, and thereby potentially more gratifying, to the wearer himself. One is the interplay between a man's trousers, shoes and socks. Another is the combination of the jacket sleeve, a half inch of shirt cuff, and cufflinks or a nice watch. Of course the latter is not possible if your shirt sleeve is hacked off at the bicep.
The more suitable (no pun intended) alternative is to wear a proper dress shirt made from a summer-weight breathable fabric like voile. (For more information on fabrics for shirts, read A Discourse on Shirtings by Alexander S. Kabbaz.) You will remain perfectly comfortable in the summer heat, and you will not risk being mistaken for the Flight Dynamics Officer at Mission Control.