I believe you will need advice from someone in Sweden, but as far as I know it isn't quite as complicated as that. Then again, I only ship stuff via the postal company and haven't tried any of the other services like DHL.
Goods can still travel rather freely within the EU (no declarations needed or anything) so the main thing here is simply to make sure that you choose a method with tracking, and perhaps buy insurance for Nirvanas and other expensive ponies.
I mostly ship inexpensive or zero value stuff, but I hope this helps. For any mail going outside the EU, I will need to fill in a customs declaration (the adhesive green form you mentioned, we still have those as well as the option to do it online and print out) AND in addition to the form I will need to register the contents online (= basically enter the exact same information I write on the form). Check with your shipping company whether you'll need a CN22 or CN23 form (it depends on the value and weight of the parcel). If you are selling, the important thing is to be honest when you fill in the information - do not mark it as a gift if it isn't, and enter the exact amount the buyer paid for the item. This is for you and your buyer's protection. Unfortunately, for any expensive ponies it will likely mean huge import fees for the buyer, but that's how international trade is... I personally - as a buyer - try to avoid the hassle and buy from the EU these days if I can. But if it's something I absolutely must have, and cannot get "locally", I will consider going through the trouble and paying the fees... In any case it's good to discuss these things with your buyers beforehand and remind them about the fees. I've never bought extra insurance so I'm not sure how that works.
I hope someone who actually knows about shipping to/from Sweden can give you more accurate information! Good luck with your sales