Self-assembly of metal nanomembranes is presented as a viable avenue to fabricate helical slow-wave structures for millimeter-through- THz traveling wave tube amplifiers. The work coordinates three-dimensional simulations of cold helices and one-dimensional models of beam-wave interaction to determine a useful range of design parameters for the slow-wave structures. These parameters include diameter and pitch. Based on the simulation results, we fabricate prototype helices with microscale diameter and pitch. The nanomembrane stiffness and the built-in stress control the geometry of the helices.