A ferry carrying three of the four dead workers arrived in Aberdeen harbour just after dawn today, with the last expected to return on Wednesday.
The fleet of Super Pumas, of which the crashed helicopter was one, has been grounded since Friday.
Super Pumas account for around half of the passengers shuttled between North Sea platforms and the mainland.
But bosses could lift the ban as soon as Wednesday after the industry's Helicopter Safety Steering Group meets to review the situation.
Industry body Oil & Gas UK said today firms were already in an emergency meeting to figure out how to keep oil production up.
The Super Puma Eurocopter was carrying 16 passengers and two crew from the Borgsten Dolphin platform when it crashed into the sea off Shetland on Friday night.
The victims were Duncan Munro, 46, of Bishop Auckland; George Allison, 57, of Winchester; Sarah Darnley, 45, of Elgin; and 59-year-old Gary McCrossan of Inverness.
The wreckage is still awaiting examination by the Air Accidents Investigation Branch.
But the crash is only the latest in a string of accidents.
Oil & Gas UK said it had given workers "several layers of assurance" of the aircrafts' safety when they returned to service earlier this month after being grounded since last October.