Well i’m sorry it took me so long to see this thread,
I’ve made dozens of canes, walking sticks, staffs, and the like for myself and friends. Sold a couple of them as well. I’ve had them used by people with disabilities (myself included) and here’s my 2 cents.
Definately stick with boiled linseed oil. It will give you the nicest finish, and it will develope a beautiful patina as it is handled. The best way to apply it would be to place the cane (as long as it’s dry wood) in a coffee can full of linseed oil (add 1/3 - 1/4 turpentine to improve the soak-into factor,) for a week or 2 so it can soak up as much as it wants, when you are done just put the lid on the coffee can and store, it will be good for years. Think of a piece of limp celery in a glass of water and you’ll get the idea. if your stick is the right size you can also insert it into those golf-ball tubes and completely soak it, but that’s most likely not necessary. Polyurethanes tend to rub off where handle and the sracthes show up more. After a while they look dingy.
I’ve made many canes from greenwood but they do have to be dried. I found that if I lashed the cane in a bundle with pipes or other sticks, it dried straight. Depending on the design of your cane you may want a little bending or twisting.
Be sure and examine the cut end of your branch, is the center soft and spongey? No good. Mulberry worked well for me, Oak is good, Maple, good. Play around with it. One tree can furnish both good and bad branches. Strip the bark off, of course.
I reccomend using those rubber cane tips for the bottom, wood will just wear out and split, especially if it gets heavy use on sidewalks and such.
I cannot get more detailed without knowing more, is there a handle? How is it attached? is it just a bend? Is your friend a 100 lb. old lady or a 350 lb. biker?
Plan on making more than one cane, you’ll get better with practice.
That’s my 2 cents, have fun.