Wood will always need to be treated with something. Varnish has a tendencey to not allow the wood to breath as it needs to. I have a friend who trains in Jodo and has stripped the varnish from his as it allows better movement of the weapon through his hands.
I prefer oiled over varnished also since making the switch to Sei Do Kai bokuto over standard cheaper shiro kashi bokuto, not as slippery in the hand. I suppose if you're making two then oil one and varnish the other, they can both be re done depending on your own preference.
I think the oil weapons makers use is tung oil, I may be wrong but can't check as the work system is a drag and has barred me from most weapons site