If you want to wax -excellent choice by the way: you want to touch wood, not a plastic cover- the wood a light sanding will help, either toget rid of any varnish or key the surface. For varnish removal you can use 100 grit, for the final preparation I'd go for 150 or better still 240 upwards. If there is varnish, sand it back to the wood everywhere first.
If you have the spare bit of wood, sand it for a while on the 100 grit until you have some sawdust then mix in normal white glue and push the resulting putty into the smaller gaps. Leave a bit too much and take it off when sanding as this is the cheapo option and can shrink a bit when it dries. The only problems are that is that it can show up if the wood is ta different shade or type, but with white glue even the same type can show when you wax it later. There is a sovent based glue sold that does the same job and vanishes more completely, but it is quite pricey.