From my experience, because you want to avoid sulfite use in the winemaking portion of production, you're going to want to limit your skin contact times to before fermentation is complete. This way, the residual CO2 in the wine will help protect the wine from oxidation during and after pressing. Whether you want to even have skin contact time is up to you and your style choices. For example, a white wine will be direct to press with the juice fermented with no skin contact.
Also, because grapes are a seasonal product, your wine without SO2 will only survive for a limited time before it starts experiencing a lot of oxidation and VA spoilage. So you will have to employ stripping runs to process all your wine quickly to an alcohol you can store for your slower vodka runs, or distill a small percent of your wine and add it back to fortify the rest of the wine lot. I've heard that the latter is more time economical, but the quality of vodka is poorer, but I can't speak from experience.