Our modern boiled linseed oil available at hardware stores etc. has modern additives ( don't eat it ! ) that allow it to dry eventually which seems to take a good month on my kayak frames.

Fine Wood Working magazine had an article in issue #64 about different finishes on wood for resisting moisture vapor which is more of a concern for indoor furniture than paddles. Linseed and tung oil were very poor at reducing moisture vapor but were rated as being good for liquid water and staining from dirt. And when a mixture of varnish and oil was used it dramatically improved the moisture excluding effectiveness of the finish. Three coats is the minimum recommended

I've used a varnish, linseed oil and turpentine mix with good results on both paddles and kayak frames.