It seems that the wires prevent the drones to go further inside the ship, so I wonder if they can be made wireless? If radio is not working in such conditions maybe sonic or light signal can get through?
At the time, the technology was not nearly trustworthy enough to run the millions-of-dollars ROV untethered.
Nowadays, we could probably build it smaller, untethered, and semi-autonomous (but that hunch is not intended to undercut the tons of work it would take to do it).
In broad strokes, how would you do such an endeavour? At those depths it seems impossible, unless some massive technological breakthrough has happened very recently.
Acoustic signalling for control (which would have to be done very carefully to account for echo, motor noise, etc), with a great deal of onboard navigation via LIDAR and onboard cameras. Signalling would be high-level.
It's entirely possible data couldn't be delivered back to the parent machine until a physical connection could be established; not sure if acoustic signalling can be made high-bandwidth enough for video. Line-of-sight laser modulation could be used for high-bandwidth once the ROV is out of the bulk of the ship.
Remote control with acoustics is undoubtedly feasible. Getting a return picture so you're not doing it blind is probably not. It would be much easier to make the drone autonomous and self pathfinding, but even that's quite state of the art and would be placing a lot of faith in your code to not get confused/lost/crash in the process.
Radio is very poor underwater. Especially deep water. Ultrasonic communication can be used, but probably not suitable for exploring the interior of a shipwreck - probably needs line-of-sight to work properly.
This is a very fun fact because it describes why we see the wavelengths that we do!
Visible light is pretty much just the portion of the EM spectrum that is poorly absorbed by water [0] (and that is also produced by the sun and also poorly absorbed by atmosphere)
If radio worked well in water (where eyes first evolved), then we would just "see" radio waves (except in practice the Sun doesn't make enough of them that reach Earth).
Nowadays, we could probably build it smaller, untethered, and semi-autonomous (but that hunch is not intended to undercut the tons of work it would take to do it).