With respect to modifying the noise toy, the hard part is powering a device on the same line it sends audio down. Unlike a condenser mic where the mic supply naturally has the audio superimposed on it, the audio chip may not like that.
If the supply to the toy is low impedance, it will short the audio. The hard part is blocking audio while passing DC, since audio is a low frequency.
Without knowing the toy power supply requirements, I cannot calculate the values needed. The resistor value will be whatever value is just high enough that, if placed across the audio line to ground (since the supply cap is essentially doing that), would not kill or distort the mic or toy audio ~ probably around 10k or 20k. The cap would be based on the toy current requirement and how fast you need it to charge from that resistance (how many times you want to send noises in a row).
I think this is quite doable if you don't plan to sit on the toy buttons all day. The only question is how badly do you want the toy on that radio.