Minor correction - I'm gluing up the blank to be 1.25"x1.25", then planing to the right shape (oval at handle sections, round for a ferrule in the middle, etc.)

I have built two kayak paddles as per B&B Yacht Design drawings included with the "Diva".  I made the shafts with birdsmouth method using 8 staves of Western Red cedar 14mm x 7mm. After planing off the octagonal corners and sanding round, the shaft is 1 3/8" D. The blades are 4mm okoume slightly arched and sheated in 1 1/2 oz glass. Overall paddle length 98" - weight is 32 oz. 

My paddles do have some flex, and for max bend on solid wood I think the "face grain" should be perpendicular to the load. You can test a strip of wood easily and I believe with load aligned to verticle grain it will bend less.

Like this.

Have fun,

Laszlo