Oak is NOT safe for birds. Acrylic and Marbella plastic are also used in toy construction. These products are considered safe as long as not ingested. This author only recommends that cotton rope toys be used under direct supervision. As the cotton rope frays, it becomes a dangerous deadly trap.
Birds can become entangled in the frayed pieces.
Injuries that have resulted from being caught in rope toys range from amputation of single digits to an entire foot. The worst cases that I know of are birds who strangled to death while struggling to free themselves. Sisal rope is a safer alternative to cotton rope. Choosing the appropriately sized toy not only increases the safety for your bird, but also increases the value of your dollars. Always start with the manufacturer's suggested guidelines for size.