Drilling was originally expected to start early last month but the Bredford Dolphin rig was delayed due to operational considerations on the preceding well, said Sunshine, which is in a 50/50 joint venture with UK partner Hurricane Exploration.
Wellington is described as a conventional target with a potentially large hydrocarbon trap, which was recognised from existing seismic data.
Wellington-1, to be drilled in 168m of water, is about 65km southwest of the giant Clair Field, which is currently producing about 23,000 barrels of oil per day, and 45km southeast of the 58,000bopd Foinaven Field.
The nearest onshore oil facilities are located in the Shetland Islands at Sullom Voe some 140km to the east.
The primary target depth is expected to be relatively shallow at about 1005m, as the location is situated on the Rona Ridge, a prominent geological feature, according to Sunshine.
The operation from rig mobilisation to the planned plugging and abandonment of the well is estimated to take about 18 days, including some contingencies.
The Wellington-1 is in a location where good quality near-shore, marine-reservoir rocks are expected to be encountered.