Let's see. Sahagún is the ending point of the Camino de Madrid and the only other camino passing through Sahagún is the Camino Francés so if you want to walk always on an official camino you'll have to walk at least part of the route in the Camino Francés. However, you don't need to follow the Francés all the way from Sahagún to Santiago de Compostela. Once in León (2 walking days from Sahagún), you can take the Camino del Salvador to Oviedo and continue on the Camino Primitivo from Oviedo to Melide where you would join the Francés once again. Another option would be to follow the Francés till Ponferrada where you would take the Camino de Invierno A Laxe where you would continue to Santiago de Compostela on the Sanabrés.
If you don't bother to skip part of the Camino de Madrid and to make part of the route out of an official camino route, you could follow the Camino de Madrid till Simancas, take the Senda del Duero from Simancas to Tordesillas (1 walking day) continue from Tordesillas to Benavente on the Camino del Sureste, go from Benavente to Granja de Moreruela following the Vía de la Plata in the opposite direction and, once in Granja de Moreruela, follow the Camino Sanabrés till Santiago de Compostela. A variant of this option would be to go from Tordesillas to Medina del Campo following the Camino del Sureste backwards (1 day walking, easy walk even backwards because you basically walk next to the motorway) and once in Medina del Campo, continue in the Levante till Zamora, the Vía de la Plata from Zamora to Granja de Moreruela and the Sanabrés from Granja de Moreruela to Santiago de Compostela.