Upvote:3
Yes - it seems to be possible to rent gear. The local Swiss tourist board website gives a list of a few shops in the area (click on Explore). The first, Wyss Sport in Kleine Scheidegg offers rental of jackets and "shoes" for the trip to the Jungfraujoch - and their shop is near to the start of the Jungfraujoch Railway.
There are a few other shops listed in other towns that offer rental of boots and sticks; these might be a better bet if you are staying in one of those towns.