The yo-yo also appears in " The Brain of Morbius ". Tom shows off his yo-yo skills with some double loops in a scene where the Doctor is having a full fledged pout. I think it's in the commentaries of this DVD that Tom mentions that when they were working on the script for that story,he was asked if he knew how to do double loops with a yo-yo.
Tom being Tom and ever happy to show off his skills, whipped out a yo-yo to demonstrate his double looping talent and smacked himself between the eyes with it.
Not to be picky, but I think it's an orange he sticks on the end of the sword as he describes Sarah as , " A girl about 5' 4" and three quarters ,probably with orange juice on her chin."
Are you suggesting coconuts migrate?