ADW Diabetes sells these: BD Veo Syringes, 31g, 1cc, 6mm. (https://www.adwdiabetes.com/product/7565/bd-ultra-fine-syringes-31g-1cc-6mm-90ct)
They're a 6mm needle, but strangely come in boxes of 90. They're not the cheapest at almost $30 for the 90, but if you're looking for a short needled...