Leaving aside the literal tons of weight a tether would require just to life a single person back to the surface (and the weight of the tether), it also could get pushed around a lot by the current. And, most importantly, once you are down there and want to navigate the wreck it would get in the way.
The weight of the tether doesn't matter when it is in water. You just design it to be neutrally buoyant. Either using mini pressure vessels or tanks of light oil.
The compressibility of water is fairly negligible - the density increase is only 1% for every 2 kilometers of depth. And obviously the cable also compresses at depth - probably by a similar percentage,
The metal wires in the tether is heavier than water. This is balanced by twining air/gas hoses into the tether. Gas compresses by 50% for each 10 metres of depth in water, so that's a whole different scale.
You either put floats (ie. Gas chambers of fixed volume) or sealed tanks of a light liquid, for example kerosene.
For high depth like this, tanks of a light liquid are probably most suitable. I'd probably use liquid butane. With a vapour pressure of 40 psi, it is easy to contain, and is has a density of only half of water. If it leaks, there won't be an environmental cleanup cost either.
