The current gain hFE on a datasheet is used when a transistor is used as a linear amplifier with plenty of emitter-collector voltage.
A transistor used as a switch (like you are doing) must saturate and the datasheet says then its base current must be 1/10th its collector current.
Then the total base current must be 0.45A and the base current of the 2n4403 must be 45mA. One 2N4403 will be fine.
re-calculate the 10 ohm resistor value.
Can your signal source produce 45mA?
Why not use a logic level Mosfet?