I keep using the term "lashing", but the method I propose may be more familiar if it is called "whipping".

You would whip the ends of a rope to keep them from fraying. The same pattern of wrapping string can be used with sinew to secure the pieces of your 2-part paddle. I hope the illustration shows clearly how you start with a loop and cover it with the bulk of your sinew or string, then catch the end of your string in the remainder of the loop. and pull on the starting end to bury the final end of your material under all the wraps.

Hope this helps

PGJ