Try intersportrent.ch
Intersport is a sporting goods chain here. We have had great success renting ski equipment from them for out of town guests.
The site is in German, look under Wandern for Wanderstock
Choose your location, you can even make reservations. They don’t seem to be expensive to me, and if they save you from slipping on your hike then I’d say it is well worth the investment!
I use hiking poles for all kinds of hikes, they help to give your arms a bit of exercise and help with the weight of your backpack (I usually carry camera equipment) as well as keep you more sturdy on your feet. They are very popular in Switzerland, you won’t be the only ones using them!
Edited to add: If it was me I would get a pair each. If you were to slip or wobble when stepping on your ‘off’ side then the pole is not much help - it would be just the same as walking without them.