You shouln't have problems to make that route. You can follow the Camino Natural del Duero (not a camino to Santiago but a GR; the GR-14 to be specific) from Puente Duero (or Simancas) to Zamora. For info about the Camino Natural del Duero (tracks, stages...), you can take a look at
www.magrama.gob.es/es/desarrollo-rural/temas/caminos-naturales/caminos-naturales/sector-noroeste/duero/default.aspx (you would be doing from the stage 15 to the stage 18 although on the stage 18 -Toro-Zamora-, instead of following the Camino Natural del Duero, you could follow the Camino de Levante).
There's plenty of accommodation in Tordesillas; including a pilgrim albergue (because Tordesillas is on the Camino del Sureste). In Castronuño, there's also a pilgrim albergue (because Castronuño is on the Camino de Levante) and there are several casas rurales although verify whether you can book just a room in (any of) those casas rurales or you have to book all the house (in which case it would be really expensive). It might be a pensión too in Castronuño but look online and double-check it beforehand. Toro has a good choice of accommodations too.