The loss of five posts was announced in May and the council-run college could only find four through natural wastage and voluntary redundancy.
Ronnie Smith, general secretary of the Educational Institute of Scotland, said last week: "We will examine every possibility including industrial action. "
The job losses at the college are part of Shetland's strategy to cut spending by up to Pounds 5 million. A controversial review of the education department is being conducted by outside consultants.
Mr Smith said: "I do not object to anybody reviewing what they are doing and their spending patterns, but it should not be purely finance driven. I do not believe that there is huge scope for savings in the education service. If it takes consultants to tell them, then so be it."
Mr Smith's father, Bill, the long-standing chairman of Shetland's education committee, is among the councillors most opposed to the external review.