I have made a few sticks and staffs. Leaving the bark on for a while will make the wood dry slower but makes peeling the bark much harder.
I made an Apple wood staff that I peeled and rough carved fresh and it dried without cracks. I may have been lucky with this one.
I tried to make a Hawthorn staff the same way and it cracked completely end-to-end.
For my last stick, Maple, I cut and peeled the bark then wrapped in 2 layers of Saran wrap tied with string to retard quick drying. This worked great. After about 4 months (stored outside during the winter), I unwrapped and started shaping...no cracks.
Most likely the type of wood has had some bearing on my experiences, but I have found peeling a green stick so easy that I will keep up with the saran wrap method for now. I have read about wood carvers soaking green wood in propylene glycol prior to carving, but have never attempted this.
I have been eyeballing my Christmas tree (Nobel Fir) top...looks like a walking stick to me. I will definately peel and saran this as the resin content is very high.
Good luck on your stick.