You say 'part of the Camino' - do you have a specific Camino in mind?
If that's just a figure of speech you could consider walking an entire camino in that time frame. The Inglès - rather appropriate considering where you're coming from.
It's just 120 km long, easily done in four to five days if you're moderately fit. Fly directly into Santiago, taxi or bus to the central bus station, take the bus to Ferrol. (In summer there's several each day, although you might want to check the schedule in case there are less in winter). Spend the rest of the day exploring - it's a lovely little town - and start walking the next morning. Or if the flights are better fly into A Corona, and take the bus from there to Ferrol.
5 days walking will get you into Santiago.
Wherever you choose to walk, Buen Camino!