As far as I know, bluetooth is an encrypted protocol, and would not introduce security issues for you. It's not wifi, it's bluetooth, by its nature talks to local devices only at a maximum of about 30 feet - and cannot possibly interact with your wireless (wifi) network.
That Logitech keyboard does not function through USB. That connection is used only for recharging the battery.
The keyboard can be paired (through bluetooth) to 3 different devices, and you only need to press a button to change between them.
I think you have a G4 iMac - no bluetooth?
You could add a bluetooth USB transmitter - plugs into one of the USB ports. But, I think you have the older USB 1.1 ports? If so, then you may find that even if the bluetooth dongle works, the performance with bluetooth might not be acceptable - plus it takes away one USB port.