Losing those warm water ports means a loss of influence and trade. Their loss would hurt more in the long run than just a few islands, even if those islands have some strategic or resource (e.g. oil and gas) value.
Really, I'm looking for a punitive result that hurts, but doesn't push Russia to the level of the Germans after WWI.
No matter what, there's going to be a buttload of butthurt. That's unavoidable.
The Kurile's are a less escalatory option, and far more justifiable internationally.
The Kuriles also are far harder to justify a nuclear response to, compared to try to force Russia to give up Sochi.
The Kuriles do not threaten the Russian heartland or cut off access to the Black Sea, and Japan has enough people sympathetic to it in Russia, partly thanks to weebery, that justifying going to total war with Japan over the islands would be harder to play at home, compared to trying to remove Russia from the Black Sea ports outside of Ukrainian territory.
This is about hurting Russia's pride without pushing to a what would likely trigger a nuclear response, and punishing them while helping an ally reclaim their rightful territory.
If we absolutely need something more than the Kuriles to punish Russian and hurt them in the long term, then South Ossetia and Konisgberg/Kaliningrad do exist and removing Russian forces from those regions is justified, if one is willing to roll the dice on whether Russia would use nukes to keep Kaliningrad from reverting to it's rightful owners after the USSR fell.
Pushing Ukraine to try to take Sochi is not necessary or useful, and there are options to punish and hurt Russia that are far less likely to result in nuclear weapons flying out of fear the 'enemy' will sack Moscow.
Plus, I do think Russia would go full Belka and nuke it's own soil, at minimum, to stop an advancing conventional force if Ukrainian was forced to attempt to take Sochi and all the Black Sea coast Russia has.
