Pretty sure dry ice is not going to do it.
The idea with freezing it down to very low temperatures is to stop any deterioration, but it is not what causes "normal" deterioration in fish used in sushi or sashimi..
Fish like Tuna are warm blooded , sort of. When the muscles need to function in cold environments, the blood needs to be very efficient. To improve its efficiency it is heated a few degrees or so above the surrounding body temperature.
This is achieved by chemical reactions involving various enzymes present in the tissue. This chemical reaction is actually triggered by the nervous system.
If you rapidly cool a tuna without first "bleeding" it you may trigger this reaction if the nervous system is intact, even if the fish itself is dead. Under theses circumstances the reaction is uncontrolled and the process will actually cook the fish particularly around backbone (where there are an abundance of nerves)
To prevent this happening in tuna, there are a few techniques where the fish is bled almost completely, using the fishes heart and circulatory system to pump the blood out. Then the brain is usually destroyed (by removal using a coring tool) and then a fiber/nylon/stainless wire is fed down the backbone from the hole left in the coring operation.. Then the fish can be cooled in an ice slurry then put in a blast freezer.
Sorry to be so long winded, but it is NOT just the cooling that does the trick of preserving the fish. A fish treated this way will keep at ice temperatures for 30 days without any discernible deterioration To keep it longer you need to freeze down to perhaps -80c. Remember, the enzymes still exist its just that they aren't activated in mass and the lower temperatures just absorb the heat they produce.
This is for tuna.
For sharks and the like (generally) there is a different reaction, again involving enzymes but the result is not to produce heat, but a bi product is ammonia. And that reaction occurs even at lower temperatures, though the temperatures do slow the process. (this is the reason not to process sharks into frozen goods, because they may well develop a ammonia smell after long time freezing).
Some fish have "delicate" texture and readily soften with time even when kept cool. (Albacore is one example, it has a fine solid texture for sushi or sashimi when fresh but its texture will tend towards "mushy" within a few days, even if treated well. That would be a case where liquid nitrogen would be a good choice.
So back to the original post. Unless the fish is already "sushi" grade, freezing will not do anything. The choice of fish will though. You want high oil/fat content fish but these oils/fats must have at least pleasant taste/smell or no taste/smell at all. Very strong smelling fish are usually ruled out unless you deliberately choose the strong smell to enhance some other aspect of the sushi. Some of the smaller mackerels and the like may also become soft with a day or so and that makes them unsuitable for sushi. Again liquid nitrogen would help but again they need to be gutted/bled cooled (in ice slurry) like the albacore.
It is more important to have processed the fish correctly in the first place. Trawl fish are usually not suitable as they are usually killed in the actually fishing and if not may die on the deck of the ship and not placed on ice for an hour or so.
Your local fishmonger may sell fantastic product, and it may be suitable for sushi immediately, but generally it has not been processed specifically for sushi.
Unless you know the fish has been processed correctly when it is caught, freezing will only extend its freezer/shelf life for normal use and it will not prevent it from deteriorating in ways that make it less suitable for Sushi/sashimi. If you are going to consume within a few days keeping the fish dry (cling wrap?) and on ice is sufficient.
(not uncovered in a fridge, that just means it will dehydrate). But just putting in cling wrap in the fridge to cool is not enough either. Best to cool it in an ice slurry, then dry and cling wrap then in the fridge to maintain the cold temperature.
Sushi & sashimi is as much about looks, texture, feel, smell as taste.