Because you have public addresses on your LAN side of the Cisco, and you are looking to have private address on your lan and you want to only use 1 device to do this, I would setup 2 VDOMs, one called ISP and the other called Private. the ISP VDOM should be configured similarly the Cisco. The output of the ISP VDOM would then go to the Private VDOM.
You did not indicate the subnet mask for the LAN side of the Cisco device, but input to the Private interface would obviously have to be in the same subnet.
You have a few more decisions to make, depending on your comfort level with the Fortigate. You will have to have either use intervdom links or physical interfaces to connect Private to ISP VDOMs. If you don' t use intervdom links you will have to put the FGT in port mode and create soft switches.
All this isn' t difficult if you really understand the FGT, if you are new to FGT, I would encourage you to work through this as it will be a great learning experience. I' ll keep an eye on this thread, good luck.
CISSP, FCNSP 4.0