I don't think I would seal it. Sealing the outside of the core will make it retain any moisture that gets inside; moisture is not good for a sword.
I believe the leather covering would be sufficient to keep the core from swelling or having any undue issues from ambient humidity or rain, lest you happen to drop it in a puddle for a while. It's not something I know much about, but based on my limited knowledge, I've not seen anything that discusses scabbard cores being sealed historically either.
There are also "rain guards" that cover the throat of the scabbard and are attached to the sword hilt; if appropriate to that time period (I'm not sure when they apply) then it may be an option if you are concerned about water getting in through the throat of the scabbard.
And nicely done!