Speedy Stitcher needle too big

Does anyone know if one can get smaller needles for a Speedy Stitcher (like an awl, but with a needle and thread for lockstitching leather)?  I need to fix my handbag, but the needle that came with the Speedy Stitcher is way too big

it's this thing https://www.leevalley.com/en-ca/shop/home/toys-and-games/crafts/50700-speedy-stitcher-sewing-kit?item=97K1050

It was probably sewn on a sewing machine. I don't know if they make smaller needles for that, but this place might have either the needles, or something else that might work for you: https://tandyleather.com/search?type=article%2Cpage%2Cproduct&q=Leather*+needles*