An article found in the November 1923 issue of Popular Mechanics (p.813) has a brief writeup on the repair of split paddle.
The article mentions that if the crack doesn't extend to far into the blade, then the split can be securely stitched with copper or brass wire. After punching or drilling staggered holes 1/4 inch from the crack and 1/2 inch apart, the blade is tightly bound or clamped so the crack is tightly closed. The wire is worked through the holes beginning at the top of the split and through the alternating holes to the tip and then worked back up through the same holes. The loose ends at the top of the split are twisted tightly and then fastened to the blade with a tack or screw. It claims an oar had been repaired in this manner and still used for another season.
In any event, might be a useful repair technique in the field if a suitable bushpaddle cannot be carved. Some wire, an awl, makeshift clamp (or string binding), and a tack might be carried in a repair kit anyway.