You can treat the wood with mineral oil, or Liquid Paraffin B.P. as it is called in Australia. The B.P. means that it is food grade. Available from any chemist in 200mL bottles for something like $5, and it it almost odorless and it is non-allergenic and non-toxic. It can be mixed with beeswax, but the beeswax will have a slight odor. Probably not objectionable though.
I gather that mineral oil sinks into the wood pretty successfully and dries quickly. It is used a lot on wooden cutting boards and children's toys. Does not go rancid which is a potential problem of the vegetable-based oils.
Richard.