but any guidance would be appreciated
There is the crux of the matter - guidance. The FMC provides the lateral & vertical guidance to fly the STAR. Most of the waypoints are not defined by a radial & DME distance, just a lat & long, so while you could theoretically fly some STARs manually, it wouldn't be very accurate & the workload would be very high. You would also have to ensure you made the altitude constraints manually too. Some seem to struggle with the altitude requirements when they have VNAV, so without it it would be really interesting. The old skills have all but disappeared.
The GPS's only provide input to the FMC position in the Boeings & can't be used for tracking, as the ones in GA aircraft can.