I fly to Sweden once or twice each year in a PA-28, VFR. The essential thing is to have time in hand - a 'spare' day for every one you plan to fly. Keep the flying days short - 3 Hrs a day means you need 3 days to get there, and 3 days to get back. Yes you can fly more - I've done Skavsta to UK (10 hrs) in one day, but it is very tiring.
All this means that you actually need 2 weeks to do this in comfort, and a budget for hotels and cabs to match. Maybe you can trim some time out of that, but when you see the fronts advancing across the N Sea toward you, you need time to sit it out.
Would an IR help? Obviously, but most things that stop you VFR - fog, low cloud, high winds and thunderstorms - will stop you IFR as well (read 'icing' for low cloud). In my view, you can go anywhere in Europe VFR as long as you have time.
And yes, you can land at Skavsta. A little expensive, but compared with the cost of getting there, a mere bagatelle. Very nice people and good facilities right on the airport.