I think you are asking about classical theory of light. Unfortunately this never quite made sense.
You might do better with quantum theory, but unfortunately this makes even less sense. It does generate answers that fit experimental observations though.
I will try to say something that attempts to fit the classical view.
Light is a force that acts perpendicular to the direction of travel. When you have a nice sine wave that's linearly polarized, it first pushes charges in one direction and then it pulls them in the other.
When it comes through a slit, diffraction spreads the light in all directions. Straight ahead it has maximum force. Off to one side is a place where some of the light is delayed one full wavelength and it cancels. Further to that side is a place where some of the light is delayed a wavelength and a half; 2/3 of it cancels and the other third shows force. Another cancellation, then a place with 2.5 wavelengths, 4/5 of it cancels and 1/5 shows force. We talk like it travels equally in all directions but the large majority of it cancels. However you interpret it though, the results are compatible with experimental evidence.
Your picture should not fully cancel because the two beams are not parallel. They will have their force in different directions and the parts that are different can't cancel. You could maybe fix that with some sort of half-silvered mirror arrangement. That looks tricky. Let's just assume it works.
Two forces act on a charge and exactly oppose each other. Do they cancel?
Imagine you have a mass with two ropes tied to it. They are being pulled in opposite directions. Do the forces cancel? Yes, they are not moving the mass. No, if you tie a new rope and pull on it, it will not act on the mass as if the other ropes were not there.
If you push on the mass, it moves. If you push on it the same amount in opposite directions it does not move. The forces cancel. But if you add a new force it isn't like the old ones are not there.
When the force from light cancels, is it like it isn't there? I don't know. Light isn't like a rope. Or maybe it is.
If you could get masers with a frequency of 1 hertz, and if you could arrange them to cancel, you could aim them at a charge. At one time they would be pushing it in opposite directions. Half a second later they would do nothing. After another half second they would be pulling it in opposite directions. And then nothing. Maybe you could tell something about the behavior of the charge. Maybe it would somehow change. Or maybe not.