Power supply design

Please can someone give me some advice on the following:

I have just finished design for the circuit on vero board and have a couple of questions about the power supply

I am thinking that I can do away with the 1000uf caps and the 1N5060 diodes which form the power supply on the diagram at


and simply use a 9V PP3 battery for DC power. Connecting directly to pins 16 and 7(through LED). Please can you let me know if I'm correct?

Similarly could I use the existing power supply as is, connected to the 9V PP3 battery for extra DC smoothing.