Hi!
You could try the Camino Ingles. There are 2 routes - one starting from A Coruna (usually 3 days) and the other from Ferrol (usually 5 days). They meet in the middle and go down to Santiago, so a map of both routes is like a letter 'Y'.
The A Coruna route will not earn you a Compostela if that's important to you, but the Ferrol route will.
The Camino Ingles is much quieter than the
Camino Frances, so there would not be so much company and accommodation is more limited. However you can walk a full Camino in the time you have!
To get to the start you can fly to A Coruna or Santiago. The train from Santiago to A Coruna is only about 50 minutes so if it was cheaper to fly both in and out of either city it's not a problem.
Buen Camino!
p.s. You could also walk between Santiago and Finisterre in about 4 days.