I use non-precessed.
For my own personal chart -- I'm 71 now -- this means a full degree's difference, or around a day in timing of the SR -- I find the same old natal position does just fine.
Using a precessed Sun, the assumption is that the imprinted point is sidereal -- it lies somewhere out there among the stars.
When a non-precessed chart is cast, the assumption is that the imprinted point is related to the equinoctial point.
Best way is to answer your own question by casting both types of chart for a sampling of significant years in the life and observing which chart best describes actual events, the same process you would use to test birthplace against relocated charts.