I will have to answer with what @elemtilas predicted: "Could a system like this be made" because you have said that it already happened through handwavium. I will begin with some conceptual issues with the framing of this question, but in the end I hope the underlying problem asked will find an answer. Bear with me.
This question treats human blood as if it only carries oxygen to cells, but this is not true. What your system is missing is, well, a lot. But mostly, it is missing the very concept of circulation, which requires pressure differentials, which require containment. In other words, you can not do away with a closed system and a pump, and still use the word "circulation."
Veins are controlled by the nervous system to target areas of the body which need nutrients, antibodies, oxygen, hormones, etc. They also target areas where excess waste has collected, such as dead cells, carbon dioxide, toxins, etc. If you remove the closed system, you take away the nervous system's only tool for getting these provisions to; and removing these wastes from, the areas of your body which need attention.
The closed system also is the only way the oxygen can possibly reach human body cells, because once open to the air, the oxygen will be taken up and absorbed. Only be being contained in veins can the hemoglobin get oxygen to the cells as oxygen. If you design your fluid so it does not oxidize, then you have also designed it so a human cell can not oxidize with it, and killed all human cells. The thing in the fluid will not be made of human cells.
A circulatory system must be a circuit, which is in the very definition of it. A free-flowing fluid would not sustain any organism which could still be considered "human;" anything adapted to that environment would look, behave, and function in a way that would be unrecognizable as "human."
If the problem in the question is simply one of respiration, as it seems to be, and you do not want to concern the plot with buggering up all the other circulatory functions, then
the fluid you are speaking of has already been found. It is called perfluorocarbon
This is technology we are already using to replace human respiration in people who cannot use their lungs for one reason or another. It seems to fit the technical requirements of your problem, from the perspective of providing oxygen to the body.