The best part (most beautiful) of the del Norte is the stretch from Irun to Bilbao - I would not recommend skipping any of these stages.
If you want to save some time just past that stretch, you can take the subway from the center of Bilbao to Portugalete and shave off about 15km (though it was quite an enjoyable walk along the river for me.) As for the rest, the area in and around Santander is pretty ugly, so I would feel free to skip that, too.
But if you only have 21 days, you will have make some hard choices. I took a train from Ribadesella to Oviedo to do the Primitivo, so cannot comment about the del Norte after that point. But from what I saw, based solely on natural beauty (and food, which is really only good in the Basque country), this is what I would recommend:
1) Irun to Bilbao (appx. 7 days), then take a train or fly to Oviedo
2) Oviedo to Santiago (appx. 12 days)
That would leave you an extra day or two to spend in, say, San Sebastian, Bilbao, Oviedo, Lugo, or Santiago, all of which are worth exploring.