Reconstruction kernels in computed tomography (CT) affect spatial resolution and noise characteristics, introducing systematic variability in quantitative imaging measurements such as emphysema quantification. Choosing an appropriate kernel is therefore essential for consistent quantitative analysis. We propose a multipath cycleGAN model for CT kernel harmonization, trained on a mixture of paired and unpaired data from a low-dose lung cancer screening cohort. The model features domain-specific encoders and decoders with a shared latent space and uses discriminators tailored for each domain.We train the model on 42 kernel combinations using 100 scans each from seven representative kernels in the National Lung Screening Trial (NLST) dataset. To evaluate performance, 240 scans from each kernel are harmonized to a reference soft kernel, and emphysema is quantified before and after harmonization. A general linear model assesses the impact of age, sex, smoking status, and kernel on emphysema. We also evaluate harmonization from soft kernels to a reference hard kernel. To assess anatomical consistency, we compare segmentations of lung vessels, muscle, and subcutaneous adipose tissue generated by TotalSegmentator between harmonized and original images. Our model is benchmarked against traditional and switchable cycleGANs. For paired kernels, our approach reduces bias in emphysema scores, as seen in Bland-Altman plots (p<0.05). For unpaired kernels, harmonization eliminates confounding differences in emphysema (p>0.05). High Dice scores confirm preservation of muscle and fat anatomy, while lung vessel overlap remains reasonable. Overall, our shared latent space multipath cycleGAN enables robust harmonization across paired and unpaired CT kernels, improving emphysema quantification and preserving anatomical fidelity.