Barium Chlorate isn't particularly hard to handle. It is however more sensitive that potassium chlorate, despite being a rather sluggish oxidizer. It's harder to make due to a poorer current efficiency. Potassium chlorate can be made in upwards of 90% or so current efficiency. 90% of the electrons go toward making chlorate, and are not lost in unproductive ways such as chlorine loss, oxygen production, etc. With barium chlorate, this value is closer to ~50%. I don't know how it's made industrially, but in small scale it's almost always synthesized from sodium chlorate or another chemical method as far as I'm aware.
I did see one reference stating that barium chlorate is less soluble in cold water than potassium chlorate, thus making the transformation you want to do impossible. However, the numbers I saw as far as solubility data did not back this up.