as long as all the planks in your core run full length, using just epoxy (IN THE CORE) will be fine.
shear loads are relatively low. Also, flexural modulus and strength (of bamboo?) are pretty good.
Hawaiis does it all with wood, but i think you should consider it your "factor of safety".
the core is pretty thin compared to Hawaiis (8mm vs 25mm) so that will be a problem w/o lots of reinforcement on the surface. maybe 10X more flexible due to geometry differences.
(moth foils are very similar in size, so a good example. a google search will find other examples in the moth forums)
once you get a handle on that we can talk about whether you want glass or carbon and make a guess for how much.
also look at the kind offering from Europe2:
you won't need to get it right the first time.
he's given you a way to compare the stiffness of your strut with others.
if you are not satisfied with the results you can add more fibers before the board ever gets wet.