Q: How do I determine the handedness of my single particle reconstruction
A: Unfortunately the normal experiment, many images of untilted specimens, doesn't provide any experimental data permitting you to determine handedness. That is, the image of a particle in a particular orientation is exactly identical to the image of the particle rotated 180 degrees with flipped handedness.
So, you must use some sort of 'trick' to determine handedness. The only way you can avoid having to do another experiment is if you have some sort of external information. For example, if you have a structure at sufficient resolution to confidently dock in a PDB model, and you can come up with a homology model or crystal structure for some component of your reconstruction, you can use the docking process to identify the handedness.
Barring that, there is no way of avoiding another experiment. There are a few accepted approaches for this. You could do a random conical tilt experiment or the newer +45/-45 tilting technique, but personally I prefer the idea of using tomography. If you have access to a microscope configured for tomography, where all of the handedness issues have been worked out for you. Then you simply do a tomographic reconstruction of your single particle specimen, and hope the resolution is sufficient to distinguish one hand from the other.
Sorry there isn't an easier answer.