If I understand your question, you’re asking how the oxygen molecule physically gets from the haemoglobin in the vascular compartment to the cells in the extra vascular compartment. The answer is blood plasma. The fluid that cells are surrounded by is the same fluid that is in blood vessels because capillaries are permeable to plasma. The oxygen is in solution in the plasma. When it is used up by cells, it is replenished by the oxygen bound to haemoglobin.
You may wonder why then have haemoglobin at all? Why not only have plasma circulating with oxygen in solution? The answer is that very little oxygen can be stored in solution. Haemoglobin evolved to increase the oxygen carrying capacity of blood.
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