Assuming this giant ball of water can hold itself together due to cohesion, wouldn't you still feel the pressure from...well, simply the water molecules themselves, moving randomly in all directions?
This is a pretty unrealistic assumption, and showing what would happen should help explain how.
The cohesive forces allow for a surface tension, which can maintain a pressure difference between the sphere of water and the outside. The pressure difference due to surface tension between an inside and outside fluid and gas surface is known as the Laplace pressure. The Laplace pressure for a sphere is given by the equation $$\Delta P = \gamma \frac 2R$$
where $\Delta P$ is the pressure difference between the curved surfaces, $\gamma$ is the surface tension of the liquid, and $R$ is the radius of the sphere. We can assume in the vacuum of space that the external pressure is 0, so the value of $\Delta P$ will represent the total pressure inside the sphere, if we assume only the cohesive forces are acting.
Now if we look at the surface tension of water, $\gamma_{\text{water}}=71.97 \ \frac{\text{mN}}{\text{m}}$ (I'm assuming standard conditions to illustrate the point; but realistically due to reasons below, I don't think you can calculate the actual surface tension of liquid water in the vacuum of space) and the Laplace pressure equation, we can see part of the problem. Let's assume the sphere is 2 m in radius, since that is likely the smallest radius you could even consider it swimming.
$$\Delta P = \frac {2}{2 \ \text{m}} \cdot71.97 \ \frac{\text{mN}}{\text{m}} = 71.97 \frac{\text{mN}}{\text{m}^2}$$
which is only $0.07197 \ \text{Pa}$. Atmospheric pressure is 1.4 million times greater (and it only gets lower with increasing radius unless you consider gravity). So to explain that aspect, if a giant ball of water could keep itself together through cohesion alone, it wouldn't really feel like any pressure at all to swim inside it.
But that probably doesn't solve all of your confusion, which relates to what I mentioned at the beginning. The unrealistic assumption is more that water would remain a liquid in these conditions at all. It cannot hold itself together due to cohesion, as liquid water at these pressures. It will want to change phases, as mentioned in the other answer. This will all depend on the thermodynamic effects of the fluid, not as much the cohesive effects. It should be pretty easy to see that at low pressure, (such as the vacuum of space with minimal cohesive force) you cannot even have a liquid phase of water. see here for an image
Best Answer
Working out how much force is required to move through a fluid, whether it's air or water, is surprisingly difficult because there are two effects you need to take into account. However neither of those effects is pressure (or at least only indirectly related to pressure).
The first effect is viscosity, which is simply how thick the fluid is. Obviously it's harder to move through a viscous fluid like treacle than through a thin fluid like water. Non-zero viscosity means that as you move you feel a viscous force.
The second effect is inertia. If you move your hand through water then the water in front of your hand has to start moving so it can flow out of the way. This means you have to accelerate the water, and because water has a mass Newton's first law tells us you need to apply a force to accelerate it. You feel this force as an inertial force.
However neither of these forces directly involve pressure. There is an indirect effect for compressible fluids like air because as you increase the pressure the air becomes more dense. As the air density increases its viscosity increases so you feel an increased viscous force, and its density also increases so you feel an increased inertial force. So all that pressure does indeed make the air harder to move through, but only indirectly.
If you now consider water, this is almost incompressible and its density doesn't change much over the pressure range humans can tolerate. This means the force required to move through water changes hardly at all with pressure. You say it's harder to swim the deeper you go, but then scuba divers can swim down to 300m depth where the pressure is about 30 times the pressure at the surface - admittedly 30m is a more sensible limit for recreational diving, but that's still 3 times the pressure at the surface.