Remote controlled miniature 3 frequencies generator

Basically I need to be able to generate 3 different frequencies (10Hz, 400Hz, 10kHz) that are 5Vpp with 0.01-0.03mA. All 3 frequencies need to be independent of each other, meaning each one can be turned on/off irrelevant of the state of the others. Example, all can run at the same time, or just 2 can run at the same time or any combination, etc. The frequency generating circuit needs to be able to fit on a PCB about 1inch x 2inches size, be able to run for 60 mins and can be controlled in a very simple way from a remote control. The frequency generating circuit will also should also be powered by a small replaceable DC battery , Lithium-Ion most likely. I think the remote can be made to have simply 3 buttons , one for each frequency, where each button turns each frequency on or off. It should be able to operate within 10ft of the the frequency generating circuit. Attached is also a small conceptual diagram that I came up with... Of course there might be other and more efficient or simple ways to do this ...Please advice! What is the simplest and smallest way built this? I would like to built a functional prototype by the end of this month. Thanks!