Body powered hand prostheses require high physical user effort. This is caused by the stiffness of the cosmetic covering, or cosmetic glove. This paper aims to present a new concept of a mechanism for the compensation of the nonlinear stiffness of body powered hand prostheses by using static balancers with a nonlinear behavior. This concept is based on a cooperative action of snap-through behavior in multiple bi-stable spring mechanisms to create the nonlinear balancing force. To demonstrate the efficiency of the concept, an optimized design for a case study of a child-size hand prosthesis is also presented. A pattern search method was applied for the optimization. As a result, the calculated stiffness and thereby the operating effort was reduced by 96%. It can be concluded from the conceptual and numerical results that the presented concept provides a highly efficient solution to the discussed problem.