If Scotland becomes independent will the Shetland Islands return to Norway?

There is evidence admittedly dated, that the Shetland Islanders are not too keen on the European Union and only remain part of Scotland as long that country remains part of the United Kingdom. If the the UK were to break up and Scotland becomes independent would the inhabitants of the Shetlands elect to return to Norway?
The Shetlands were given to the King of Scotland by the king of Norway as part of a dowry in the middle ages. Norway is not a member state of the EU.