I called the people at CA-Boden today (they're the ones with the mini-Funkis) to talk about a possible shed. Somehow, I rang through to their director, Christer, who was a little nonplussed by my American accent, but agreed to send me an email for a quote for a small shed.
I asked for something about 6 square meters, not insulated, with a window and a door, delivered to Djurö. Janne suggested I insulate the shed (or at least a portion of it) because I could keep freezables like paint in there more safely. But I thought I'd get a non-insulated quote as I still have 4 bales of insulation stored under the house from our original construction.
When I hear from Christer, I will of course report back!