The actual answer to your main question.
Given that the wights are able to survive in water, it's perfectly possible for them to sink down to the bottom, attach the chains to Viserion, and then walk to the edge of the lake where other wights could have broken the ice so that they can exit. Or they can climb back up the chain.
Or if the lake is not easily walked out of, they are simply are stuck there and no one cares. The Night King isn't known for his caring attitude.
Most of your question is based on Euron's question about their ability to swim, but your assumption here is wrong. When a human asks the question "can you swim?", he can mean the following things:
- If I put you in water, can you survive (by swimming)?
- Can you stay afloat?
- Can you move around in the water?
For humans, all three are the same thing. We need to move around (upwards), in order to stay at the top, so that we can breathe (and therefore not die). But this is not necessarily the case for wights. So Euron's question (and the answer it receives) hinges on the interpretation of "swimming".
Define "swimming" for wights.
1. Can the wights survive in water?
Yes they can. This is evidenced by (S07E06) the wights who rose up out of the water to try and drag Thormund down. Being submerged in water does not kill a wight.
2. Can wights stay afloat?
As far as we've seen, and can logically deduce, most of them cannot.
From what we have seen, wights sink into the water immediately (as evidenced by S07E06).
There is the question of how the wights managed to come back up top (when dragging Thormund down). Though not explicitly shown, it's possible that a sufficient amount of wights has fallen into the water, that they basically made a human pyramid (erhm, zombie pyramid) to get back up.
Note that while we did not see it happen underwater, the wights who attacked Jon in S07E06 (who was standing on the raised edge of the island) did actually pile on top of eachother in order to get to Jon, so there's at least some precedent for the wights being able to use "ant tactics" and use eachother for climbing.
Frow what we can logically deduce, wight have either no flesh, or less flesh than humans. Flesh is more buoyant than bones, and therefore a human is more buoyant than a wight. When comparing fleshy wights to skeletal wights, you'd expect the former to be slightly more buoyant than the latter (though still less than a human).
3. Can wights move around in the water?
Similar to the buoyancy argument, wights will be considerably less able of doing so than humans, and skeletal wights will be considerably less able than fleshy wights.
The wights are denser than the average human, and therefore sink faster. This means that a swimming wight would have to already swim better than a human, due to needing to counteract gravity more.
Moving around in the water is done through "paddles". Flat pieces of surface that are used for pushing off against the water (essentially the same as a wing). A duck's webbed feed, the oars of a boat, a boat's propeller blades, a swimmer's hands, ... all of these examples try to maximize the surface area in order to increase their efficiency.
But wights are barebones (pun intended) as far as paddles go. They are thin and dense, which is the exact oppose of what you want (large and not too dense).
Fleshy wights who still have full arms and legs may be able to still use them as paddles, but they would still have to be better than humans (due to sinking faster), and it's even possible for the necromancy (however it works) to not understand how swimming works in the first place.
Conclusion about the swimming.
Wights can survive in water, but they are mostly incapable of moving around in water. It stands to reason that they can walk on the bottom though.
We can't know which definition of swimming Euron was focusing on. We can somewhat deduce that whoever answered the question (I'm not sure who it was) was thinking about moving around in water, not surviving.
Also note that if the wights were keen on travelling through water, they could easily have circumvented the Wall. Most of the argument as to why they did not circumvent it relies on the impracticality of doing so (no fleet, it creates a bottleneck, ...) but those arguments go out the window when they can just walk on the ocean bed like it's nobody's business.