When you're planning to travel by airplane, you can take your walking stick right onto the plane with you.
Many airlines allow you to take a walking stick onto the plane, and it won't be considered your one allowable piece of carry-on luggage. A walking stick, like a cane or a pair of crutches, falls under the category of a mobility device. There's little restriction on such safety- and health-related items, including walkers and child-restraint seats. Airlines such as United do not count assistive devices as carry-on luggage.
When you board the airplane, ask a flight attendant if she can store your walking stick for you. Many airplanes have closets to store long or irregularly shaped passenger items such as hanging garment bags, walking sticks and canes. Toward the end of the flight, the flight attendant will return the walking stick or you can ask for it.
To help avoid unseen circumstances at the airport, contact the airline you'll be using and ask about its specific policies concerning walking sticks. Ask whether you can keep the walking stick with you on the plane, rather than have to check it with your suitcase.