Modification of dome light to add pull switch?

Thank you one and all.....I'm not keen on the remote, that is why I was looking at the pull string.

I would love to have two wall switches, since we have two doors into the bedroom (his & hers).....however there is no place to pull the wires down to the switch. The bedroom wall is all wood and the back of the entertainment system....if anyone has any other suggestions, I would love to hear them!