Is wood stain okay to put in a hamsters cage?

For my hamster, I have a glass aquarium. Im building 2 new levels to it today to give her more things to do and more room..the wood, I got it from Hobby Lobby. Im using wood dowels for the legs, and a wood hanging door sign for the platform. I dont like the way the wood looks. Its kinda white, and ugly. I have to go to the store today to get some popsicle sticks for the ladder, and while im there can i pick up some wood stain?