Ferry or flight from Tallinn to Stockholm?

You don't have to choose between seeing the Stockholm Archipelago and preserving most of your sightseeing time in Stockholm. I think you'll find there are overnight ferries.

I've taken such ferries twice between Stockholm and Turku, Finland. The Viking ships were fine; I assume Tallink Silja is fine as well; the companies use different docks, so it's worth taking a look at a map to see which one looks most convenient. The cheapest cabins are small, but you'll have your own toilet and shower, and there will be hot water. I've never had trouble sleeping on a ferry (as opposed to sleeping on an overnight train).

When comparing ferry vs. flight costs, don't forget the expense of getting to and from the airports. I trust you are aware the budget airlines will charge you for everything they can possibly come up with, so be sure your suitcase/backpack and carry-on bag are tiny enough to fit their size limits. If they are not, flying could be more expensive than a ferry.

You could take the ferry over to Helsinki and see the city. Then take another overnight ferry to Stockholm.

Or you could fly. Either way would be fine.

No, the ferry is not more expensive than flying!

You need to look at the total cost, including travel to and from the airports and additional Ryanair fees. And remember that the ferry is overnight and flying means you have to pay for an additional night in a hotel room.

But yes, the ferry is a nice way to travel and gives you a great view of the Stockholm archipelago in the morning.