I have never done this myself, so I can't say this will definitely work or not, but here are some suggestions to try.
You should be able to start up the iMac in FW Target Disk Mode, where it will basically function as an external FW drive when connected to another computer.
How to use and troubleshoot FireWire target disk mode - Apple Support
Then you can perform a secure erase on the iMac internal drive, as if it were an external drive on the second computer. you could also copy and files from that drive before you erase it, if you need to.
http://www.howtogeek.com/179284/how-to-securely-wipe-a-hard-drive-on-your-mac/
If you have success with this method, please report back your results.
EDIT: not sure which particular vintage model iMac G3 you have, the FW400 ports were introduced in later models, but earlier models do not have this capability.