Spin-orbit (SO) coupling is an important ingredient in many recently discovered phenomena such as the spin-Hall effect and topological insulators. Of particular interest is topological superconductivity, with its potential application in topological quantum computation. The absence of disorder in ultracold atomic systems makes them ideal for quantum computation applications; however, the SO coupling schemes proposed thus far are experimentally impractical owing to large spontaneous emission rates in the alkali fermions. In this paper, we develop a scheme to generate Rashba SO coupling with a low spontaneous emission extension to a recent experiment. We show that this scheme generates a Fermi surface spin texture for 40K atoms, which is observable in time-of-flight measurements. The chiral spin texture, together with conventional s-wave interactions, leads to topological superconductivity and non-Abelian Majorana quasiparticles.