So you current have
PC -> USB cable -> FTDI -> TTL serial -> toy
and you want to change that to
Arduino -> TTL serial -> toy
Is that right? In that case do you know what the TTL serial configuration is (speed, start/stop/parity bits) and what messaging protocol is used over that serial link?
Or are you actually using
Arduino -> USB host shield -> USB cable -> FTDI -> TTL serial -> toy
In this case you need to know what sort of USB device the FTDI adapter presents itself as and find or write a suitable USB host driver for it - writing a USB driver is a very substantial piece of work.