No, it would not be offensive.
A survey of 200 pilgrims on the Camino de Santiago found that motivations were as follows, in order of importance:
- Peace, solitude, relaxation
- Spiritual (but not explicitly religious)
- A lifetime experience
- A religious pilgrimage (9.6%)
- To meet people.
Source: Top reasons why people walk the Camino
As you can see, under 10% viewed their walk as a religious pilgrimage, and this is on a route between two Catholic countries. In a country like Norway with only 5% of Catholics I would imagine that the percentage of religious pilgrims would be smaller still. So as a non-religious walker you would be very much in the majority.
Is this use of these old pilgrimage routes offensive to the minority who still use them for religious reasons? I know people who have completed the Camino and have read many accounts - I've never seen it even hinted that this was an issue. Provided you are sensitive to the feelings of the pilgrims you can be comfortable that no-one will object. And as Ken Graham has pointed out in his comment, pilgrimages are not a sacrament of the Catholic Church and are open to all.
So it would be perfectly appropriate to walk the route to simply enjoy the country and the experience. I hope you have a great time!
If you've ever read Chaucer's Canterbury Tales you'll know that motivations for pilgrimage have always been varied. In the regimented medieval world, this might be your only opportunity for a holiday and an adventure. As with the modern holiday industry there were package tours, guidebooks and accommodation touts.
I found the following account of the atmosphere around shrines like St Olav's and Santiago de Compostella:
At the sanctuary itself, particularly the famous ones, pilgrims would be met by a large noisy crowd. In a city like Trondheim, where many pilgrims wandered to visit the grave of St. Olav, there were many people making money from the pilgrims. Amongst the fellow pilgrims, there would be buskers and entertainers, market stalls and pickpockets, beggars and prostitutes. There were primitive postcards and souvenir pilgrim-badges to buy from licensed traders. Pilgrims showed particular interest in the exotic products, spices, wines and silks, not available at home. Many pilgrims also indulged in a little bit of 'duty free', hiding their purchases from the customs men or bribing the appropriate officials to turn a blind eye.
Inside the sanctuary, things were little quieter. As the day progressed, crowds grew and the wine flowed freely. At Santiago de Compostella, the priests despaired that 'all sorts of noises and languages can be heard together, discordant shouts, barbarous singing in German, English, Greek and every other language under the sun'. (Sumption: 213) The behaviour was such that many sanctuaries, such as Durham in England, employed the equivalent of 'bouncers' to keep order and eject those who behaviour was considered too 'rude'.
If anything, the non-religious hikers of today are more respectful than the religious pilgrims of the past!
Source: Why did people go on pilgrimages?