I have small frame pumps on my bikes but honestly they’re next to useless. Good for small tube inflations but will never bring a road bike tire to near full pressure. I’ve looked into many of the small rechargeable ones too but besides costs there’s pros and some cons to several of them and frankly for the price of those you can buy almost a full box of CO2 cartridges and carry three with you at all time. Using a small nozzle one cartridge will give you a full tire of pressure in 30 seconds. And carry at least one tube and three tire levers. A small cheap under the seat bag will do ya or a pouch stuffed into a jersey pocket.