Q: Are There Replacements for the iMac G3 (Bondi Blue) 15 Pin Video Cable?

Assuming that you mean the cable/plug shown on page 8 in https://manuals.info.apple.com/MANUALS/0/MA492/en_US/iMacG3_originalInstallGuide .PDF, it could per se probably be found through a web search for something like "iMac G3 RGB video cable". However, a warning: Replacing the entire cable would mean having to gain access to sections of the computer that are intended only for someone with the necessary expertise (dangerous high-voltage circuits inside), so do contact a service provider for this work.

"I'm not concerned with the high voltage stuff, as the machine hasn't been powered on in a few months."

A few months doesn't matter, because high voltage from the flyback transformer is stored within the CRT and has no discharge path.  Until properly discharged, you could be knocked out for the count, if repairing a CRT-type TV or display and you inadvertently became the path to ground.  The other end of the R-G-B cable connects to the analog-video board, and it's not a DB-15 connector.  The procedure for handing any components on or wires connected to the analog-video board first requires discharging the CRT.

If the plastic shaft that you turn to loosen the connector isn't visible, insert the end of a paper clip into the small hole on top of the connector to determine how far down it broke off.  Once that's determined, you could carefully cut away the plastic on that side of the connector, a little farther down than the paper clip indicated the broken bolt shank to be.  Grasp the end of the exposed bolt shank with needle nose pliers to rotate & remove.

It's called the Red-Green-Blue video cable.  There were two versions of it, depending on whether the iMac was one of the earliest models with the first version of the analog-video board.  Subsequent models having a Rev. 2 analog-video board used a slightly different R-G-B cable.

I think you cannibalize one from another imac rev a.  The rev b, c, and d have the extra 4meg of video ram.

Do you have the service and repair manual.  Once named imac.pdf?

I happen to have a non-working iMac g3 233 rev a.  I examined the cable connector. Is this the one?

Has 980808 written on the other side of the connector. When the connector is detached,  the screw moves up and down the length of the exposed screw [ the right portion ].  There is some catch that prevents you from pulling the screw out. The screw is rather free moving other than that. 

As suggested before, i'd suggest taking an exacto knife and try to shave off the bottom portion just above the metal strip. Yes, there is a metal strip the juts out and around the screws shown at the right.  I'll bet there is a metal constrainer embedded in the plastic that is up the length of the exposed screw.

Another thing you might do is to try the take the top cover off and try to work your way down.  Be careful because you will be exposed to high voltage. 

No.  That end goes into the video housing.

Send me an email & i'll see if I can email the service and repair manual.  Here are the pictures.