With the caveat that I haven't been to Copenhagen since 1972 (but have read many comments about it on this forum), I think Helsinki has less to immediately grab a traveler than the other cities. That's not to say I don't like it; I've spent about eight days in Helsinki (across two separate trips, totally planned by me) in the last two years. But it's a newer city, and if you aren't a big Art Nouveau fan (which I am), I think there's less to immediately grab a foreign visitor.
I think it's a shame to visit Tallinn for just one day; one day in Helsinki makes more sense from my perspective.
There are ferries from Stockholm to Tallinn. I've taken the overnight ferry from Stockholm to Turku twice and found it comfortable enough for a short trip; my cheap cabins had en-suite bathrooms and air conditioning. Unfortunately, the trip from Stockholm to Tallinn is more than overnighter, so you may want to consider flying. SAS has a couple of flights on the random June day I checked, but the fare wasn't cheap. I see that Air Baltic, which probably has more flights to Tallinn than any other airline, has flights from Copenhagen but not from Stockholm, so I'd look at setting up the itinerary like this: London-Stockholm-Copenhagen-Tallinn if you don't want to take the long ferry trip from Stockholm to Tallinn.
Note that ferry prices can rise a lot as the travel date approaches, and the cheapest cabins can sell out, so don't leave that until just a week or two before the trip unless you absolutely must. I ended up paying nearly triple what I should have because I dilly-dallied on buying the ticket.