I believe if you mount it along the seat stay, it would not be a frame pump, just another mini pump mounted to your frame. I would consider this a frame pump:



My recommendation is anything with a hose. Here in Canada we have something similar to a Topeak Road Morph Mini made by Filzer. I have one clamped to a seat stay on my road bike with zap straps. (The zap straps are for the mount, not the pump). If you are worried about it coming off, make sure that it has a velcro wrap around.