I'd go carefull with the nail varnish remover,it may affect the wood finish,try a very small out of sight area with a moistened tissue,even if there's no biro there.If the tissue picks up colour,don'r risk it. I'd also do the same check with the meths.
I have to use laminated target sheets at work and sometimes the staff write on them in permenent ink and so to get it off i go over to the perfumery dept and spray abit of D & G or Gucci on it and it comes off a treat