A handsaw or folding saw that you find in most garden centres and tool shops,
A pair of secateurs for trimming thorns and side shoots,
A a pair of leather gloves when working with blackthorn or hawthorn,
Rope or baler twine so you can the walking sticks in a bundle and carry them,
A spade or trowel for digging up roots,
A rucksack to carry the items.
Before you cut anything it probably belongs to someone any its always better to get permission from the from the owner to cut the walking sticks, most land owners are very good to deal with and there shoulsn't be any problems. The second rule is to tidy up after your finished cutting walking sticks, don't just leave branches and twigs lying around always clean up after you, and don't expect to be welcome back again.