Is there proof that Waknuk society has no currency in the novel The Chrysalids by John Wyndham?

No. There is no proof in the book that the Waknuk society is a society without some kind of currency.  

The contrary is true.  The Waknuk society has some kind of currency, and they call it money.  It is used to buy goods and services, and it can be obtained through the sale of goods and services.  

Chapter Two contains the book's first reference to money.  David is explaining to readers about genetic changes called "deviations."  He explains that his father is adamant that all livestock and crops that show drastic genetic change must be destroyed.  David notices that his father does this more often than other Waknuk members, but Joseph does this because he is passionate about genetic purity.  He doesn't like destroying so much of his farm for genetic purity, and he mentions that it is a financial loss every time he purifies a crop.  

He had no wish at all to throw good money away, he pointed out.

A few paragraphs later, David is telling readers about the threat of Fringes raiders.  David says that the raiders will steal mostly livestock.  Waknuk community members help the family out in a variety of ways.  One way is giving the family money. 

Occasional small raids used to happen two or three times a year, and nobody took much notice of them as a rule — except the people who got raided, of course. Usually they had time to get away and lost only their stock. Then everybody would contribute a little in kind, or in money, to help them set up again.

From those two examples, it's clear that Waknuk society has currency and uses it in the way that readers are familiar with.