reduce output power of bluetooth module (NOT power consumption)

I would like to reduce the power of the radiated signal and preferably limit the rapid rise and fall times of the signal.

Reducing or increasing the power of the output signal does NOTHING to change the shape of the output signal. If you change the shape of the signal, the receiver will no longer recognize it.

Whether you can change the output power depends on whether the hardware allows you that control. Since you didn't say what the output device is, only you can determine that.