One of my past projects involved a PIC16F84 and a HK828 256k voice recorder IC that you can get from Jaycar.
Complete in a kit:http://www.jaycar.com.au/productView.asp?ID=KC5454&CATID=25&form=CAT&SUBCATID=557
My project's PIC randomly enabled one of the registers and let it 'speak'. I just used the onboard audio amplifier and the speaker from the kit but if you want it completly silent (and the best quality) I'm probably not the best person to advice you on how to connect it.
If the pictures I found on google were correct, your icom has an RJ45 style socket on the back for 'mic'. You will be able to hook that up to a uC (or PC) that does the switching for you.
Your icom manual on page 45 (link below) shows that it uses RS232 for communication. I've seen it spit out frequencies when you simply turn the dial on the radio (you may need to enable it in the radio's menu first though).
The link to your radio's manual:http://www.radioamateur.eu/schemi/IC706mkIIg_user.pdf
Hope this helps.
(Doesn't your radio have the ability to record messages?)