We introduce a minimal model of a swimmer without body deformation, based on force and torque dipoles which allows accurate and efficient 3D Navier-Stokes calculations. Our model can reproduce swimmer propulsion for a large range of Reynolds numbers, and generate wake vortices in the inertial regime, reminiscent of the flow generated by the flapping tails of real fish. We perform a numerical exploration of the model from low to high Reynolds numbers and obtain universal laws using scaling arguments. Collecting data from a wide variety of micro-swimmers, we show that our theoretical scaling laws compare very well with experimental swimming performances across the different hydrodynamic regimes, from Stokes to turbulent flows. The simple design of our generic swimmer model paves the way to efficient large-scale simulations of hundreds of individuals, crucial for understanding collective effects within assemblies of aquatic animals.