That watt rating is not what the speaker requires or a measuren of how loud it is; it simply tells how much power the speaker can handle without burning up.

So of course two 8ohm speaers will sound identical in volume if they are equally sensitive, i.e. can produce equal decibels at same power fed into them.

It won't change how much power the circuit can output to speakers.

What you can do is to put a 6 ohm or 4 ohm speaker to get more watts into the speaker, but it is unknown if the source can drive a heavier load.

Another option is to get an 8 ohm speaker with better sensitivity, to get more decibels at same wattage.

A final solution could be to reverse engineer the circuit to figure out how to get more amplitude out of it, or how to add a separate amplifier if even possible.