I'm not aware of any studies that investigate the equilibration of oxygen saturation between two individual cells in hepatic sinusoids, but I will answer based on what we know about these issues in the general context.
See West, Pulmonary Pathophysiology, Ch 2, oxygen loading in a healthy lung occurs to full saturation in about 0.25 seconds, one-third of the available contact time:
This involves diffusion through surfactant, the alveolar membrane of an alveolar cell, the cytoplasm of an alveolar cell, the basal membrane of an alveolar cell, the basal lamina, the basal membrane of an endothelial cell, the cytoplasm of an endothelial cell, the luminal membrane of an endothelial cell, plasma, and the membrane of an RBC. (see this illustration from Ross Histology)
In the liver, oxygen rich blood arrives from the hepatic artery, nutrient rich blood arrives from the portal vein. Blood from these different sources mix directly in the same vessel in the same hepatic sinusoid. There is no alveolar cell, basement membrane, or endothelial cell in the way. Oxygen just has to diffuse across one plasma membrane, in blood, and across another plasma membrane, all in a fluid moving together.
Diffusion of a small molecule like oxygen is quite fast, and RBCs are made for rapid diffusion, even of a large globular protein like hemoglobin.