Oil-rich Shetland may consider becoming a self-governing territory like the Isle of Man rather than stay part of an independent Scotland in the event of a yes vote, the Scotland secretary, Alistair Carmichael, has said.

In an interview with the Guardian, Carmichael said if Shetland were to vote strongly against independence but the Scottish national vote was narrowly in favour, then a "conversation about Shetland's position and the options that might be open to it" would begin.

The Liberal Democrat MP, who represents Orkney and Shetland in Westminster and has been secretary of state for Scotland in the coalition government since last October, said those options might include the islands modelling themselves on the Isle of Man, which is a self-governing crown dependency that is not part of the UK, or on their neighbours the Faroe Isles, which are an autonomous country within the Danish realm.

Asked if he was suggesting Alex Salmond should not take for granted that oilfields off Shetland will belong to Scotland in the event of a yes vote, he said: "That would be one of the things that we would want to discuss. I wouldn't like to predict at this stage where the discussions would go."

Responding to Carmichael's comments, a Yes Scotland spokesman said: "Scotland's island communities will have greater control over their local economies, natural environment and be represented at the heart of government in an independent Scotland.

"A yes vote is about empowering people and communities throughout Scotland, including our island communities. That is one reason why the Shetland News has chosen to chosen to back yes."

But Carmichael's comments were echoed by Tavish Scott, Shetland's MSP, who when asked whether Shetland would have to obey the will of Scotland in the event of a yes vote, said: "Will it now? We'll have to look at our options. We're not going to be told what to do by Alex Salmond."

Speaking as he canvassed in the capital Lerwick's town centre on the final day of campaigning before the vote, Scott said the option of becoming a crown dependency was "something we will look at", though he said he ruled out full independence for the islands.

A petition of more than 1,000 signatures raised by islanders from Shetland, Orkney and the Western Isles calling for a separate referendum on whether they could themselves become independent was rejected last month by the Scottish government, which said it had promised new powers to the three island groups.

The Shetland archipelago, more than 100 miles north of mainland Scotland, has traditionally voted strongly against Scottish independence, in part because of its distinctive history – until the 15th century it was part of Norway and is closer to its west coast than the Scottish capital – in part because the oil industry has made it rich without particular assistance from Edinburgh.

Sullom Voe oil and gas terminal, in the north-west of the island group, is one of the largest in Europe, and a levy on oil processed through the islands since 1976 has poured into a multimillion pound charitable trust, which funds services, community projects and the arts for the islands' 23,000 population. Shetland's landscape and much of its architecture is unsparing, but roads and services are excellent, shops prosperous and hotels full of foreign business travellers.

If the extent of Scotland's oil reserves has been hotly debated across the nation as a whole, the topic is even more pressing in Lerwick, where the main harbour is dominated by six cruise ships providing accommodation for 1,700 workers from Total's gas plant, next to Sullom Voe.

Few expect Thursday's no vote to approach the emphatic 73% vote against independence in the 1979 referendum, however. In the bustling Yes Shetland shop on Lerwick's Harbour Street, which opened last month thanks to crowd-funded donations, campaigners yesterday rattled off detailed figures for the amount of oil remaining in the oilfields west of Scotland, and repeated the widely held claim among independence supporters that its true extent has been concealed by Westminster. A YouGov poll last week found 42% of voters in Scotland believe it is "probably true" that a bonanza find on the Clair oilfield is being concealed by BP until after polls close.

"Of course they have downplayed the amount of oil we have left," said Angela Sutherland, who had popped in for a cup of tea with fellow campaigners. It was "our oil", she said, and if independence is rejected "we're not going to get a penny of it, it's going to underwrite [Westminster's] debt".

A lifelong Liberal, Sutherland said she joined the SNP four months ago "because I felt the press coverage wasn't supporting yes, so I wanted to give them my support".

For Sue Wailoo, independence offered "an opportunity to build a country that's a fair society. We are a nation that is a small enough unit, and there are enough people with great ideas, that we should be able to govern ourselves."

But many on Shetland remain cautious, and for Gillian Ramsay, owner of the Shetland Art Company, a craft shop on Lerwick's narrow, twisting Commercial Street, there were too many unknowns for her to support yes. "I have a business, and I wonder how a yes vote would affect me. Will we be in the European Union? Will England be a foreign country? Will I have to pay more to bring in my materials? They can't tell me. This is the problem. They have been unable to satisfy me that it would be better if we were independent."

Those were all points being stressed by no campaigners a little further along the street outside the Bank of Scotland where, in a rare display of political unity, representatives from the Lib Dems, Labour and Conservatives were campaigning side by side. "We're Shetlanders and we've always lived peacefully in Shetland," explained Theo Nicolson in the strong Lerwick accent that still echoes its Scandinavian origins.

Nicolson, the local Lib Dem chairman, described himself as "Shetlander, and then British". And Scottish? A long pause. Only because his mother was Scottish, he said. "We're so different here in Shetland. Our history; we were part of Norway of course and we've always had a strong Norse background. We don't have the tartan culture here." His strong sense of Britishness comes from his father and grandfather who fought in the two wars, something that is important to many older islanders, he said.

Before retiring, Nicolson worked at Sullom Voe as a marine engineer. What was his perspective on the oil question? "Nobody knows how much oil is there. There's a vast amount of difference between different experts. And as you push out the frontiers, it gets more and more difficult to recover and more and more expensive to recover. It depends on global oil prices whether it will ever be viable, and that's something that no man knows."