Haven't posted here in forever...
There are a number of variables here:
* Making a walking stick (or anything) from the full diameter of a "stick" of green wood with the pith running through the center makes checks/cracks likely as the wood dries. Small diameters will be fine, but above a certain size (depends on species and use) they will crack.
* For walking sticks, where durability and strength really matter, consider picking a really tough, hard wood from your area (Osage Orange, Black Locust, Teak, etc...). Some woods are naturally rot resistant (like Locust), so those might make be a good choice.
For a walking stick, no finish is also an option, allowing it to develop a patina from use. If you want to protect carvings and such, read on...
* Ideally, a wood finish would penetrate INTO the wood and harden as it cures INSIDE the wood, and not form a dipped-in-plastic coating on the outside. If you actually WANT a glossy, dipped in plastic look, there are many polyurethanes or "wipe-on poly" products available at local hardware stores.
* Oil finishes should utilize a "hardening" or "drying" oil -- one that polymerizes as it dries/cures to form a sort of organic plastic-like substance that protects the wood. Some are very slow to dry, so chemical agents, or driers, are added. These often contain lead or other metals and can be very toxic.
* One school of thought is that ALL wood finishes are food safe once they are fully cured; I'm not 100% convinced of that. It depends on the use and the finish. I tend to stay away from anything with toxic driers in it -- your experience may differ.
* If you want a non-toxic finish you can use for these products as well as other bushcraft items (spoons, bowls, cutting boards, etc...), consider what sort of stuff you would be willing to put in your mouth. Some companies only make non-toxic finishes (Tried & True -- a favorite -- was mentioned earlier)
* "Boiled Linseed Oil" is generally not boiled. Many years ago it was, but heating raw linseed oil to the boiling point (to help it polymerize and harden more quickly) is dangerous, and there were too many shop fires and burn injuries to continue the practice. "BLO" contains heavy metal drying agents.
* Oil finishes have to be used properly to avoid forming a sticky mess. Many of them instruct you to apply liberal amounts of oil, then after a 15-minute wait, to remove as much of it as you can with a towel, rag, or paper towels. If you don't do this, you'll have a mess. Some say to use multiple very light coats, and wait for drying between each -- just wipe on with a rag or paper towel, then wipe off.
* Rags used in oil finishing should be considered a fire hazard! The drying (polymerizing) process releases heat, and under some conditions, they can self ignite! I tend to burn all these items in a wood stove or fire pit.
* Some oil finishes are very water repellant -- others are not. Pure Tung oil resists water, but takes a loooong time to cure -- like months. Many nut oils are so-so, but dry much faster, and are very easy to re-apply.
* NON-TOXIC HARDENING OILS: Walnut oil, Hempseed oil, Linseed oil, Safflower oil, Tung oil (careful here -- many so-called Tung oil finishes contain no actual Tung oil), and a few others. I especially like Mahoney's Utility Oil (pure heat-treated Walnut oil), Tried & True Original (Linseed oil plus Beeswax), and Tried & True Danish Oil (just pure Linseed oil with no hardeners), and have found light applications of Hemp seed oil from the health food store to work very well.
* Linseed oil is very common in Scandinavian countries for all manner of woodworking. It can be "cleaned" with water (look up on-line) which helps it dry faster, smell better, and darken the wood less, though that process takes a few weeks. Cleaning usually involves mixing with water, sand and salt (below).
* Most raw cold pressed nut oils found at your local health food store or food co-op are OK, but generally won't harden as quickly or completely as those which have been heat treated (kinda like boiling) and cleaned to remove impurities. They may remain sticky due to all the good stuff for salads that's not-so-great for polymerization. Oils intended for wood finishing will usually perform better. I haver not seen Hempseed oil that's been treated for woodworking, but the organic salad oil stuff does seem to work quite well. I may try cleaning some I have on hand...
* Scandinavian oil cleaning method here: https://www.youtube.com/watch?v=wi4YweOes5E
That's all for now, folks, hope there's something helpful in here for you.