A majority voted to ballot the rest of the workforce on accepting an offer of up to £5500 compensation by chief site contractor Petrofac.
The move comes after a similar meeting on Tuesday unanimously rejected the offer for Sullom Voe, despite union leaders recommending it be accepted. The dispute is shared accommodation and commuting.
Unite regional industrial organiser John Taylor said: "It's only fair that everyone gets a say in the matter, so they have agreed to postpone industrial action."
Petrofac said the offer was generous, adding: "We hope the membership will accept it this time."