I will be flying within USA on Southwes Air and plan to travel with a hand made walking stick with a wrist strap and rubber tip. 47 inches long. Is this something I can carryon or strap it to my checked bag?
They might treat that like a cane so you should be able to carry it on and they stick in the closet.
You can email, call or Tweet them your questions
https://www.southwest.com/contact-us/contact-us.html
Do you plan to use the walking stick on your trip or are you just taking it home?
Back in the good old days, you could have carry it on, but probably no longer post 9/11. We carried on our Mt. Fuji sticks back in the 70's.
Strapping it to your checked bag is very risky. It could get lost or broken.
Best to put the stick in it's own box with padding, then check it as a fragile item and keep your fingers crossed.
If you are going to use a walking stick on your trip, I suggest buying a collapsible walking stick which will fit into your suitcase.
Amazon has plenty of them. This is what we do nowadays.
If you are taking it home, you could go to a FedEx or UPS store and have it shipped home.