How do I get from the Faroe Islands to the Shetland Islands or the other way round? Is there anything besides a flight via Scotland?
No, the quickest route is making your way to Edinburgh and flying with Atlantic Airways from there. As pointed out by @Dorothy, direct ferries haven't been around for nearly a decade.
This flight can be booked here
Direct ferry is no longer an option, since Smyril discontinued its Shetland link on the Denmark-Iceland route which, until 2008, ran from Lerwick to Tórshavn.
You can reach the Faroe Islands:
By sea: Smyril Line’s M/S Norröna sails from Hirtshals in the north of Denmark and from Seyðisfjørður in Iceland.
By air: on either the Faroe Islands’ national airline, Atlantic Airways, and Scandinavian Airlines (SAS).