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Reconnection of sheared magnetic fields is commonly treated by regarding the component perpendicular to the antiparallel components as a largely inert guide field. In this paper an alternative is proposed in which the free energy residing in the shear field is being converted prior to reconnection. This happens in high-density, dissipative current sheets bordering the reconnection site. A global scenario is presented in which low-intensity currents out of the photosphere are converging into the narrow, high-intensity currents at high altitude. This is enabled by the obliqueness of the latter. The very short timescale of the energy conversion causes a lateral propagation of the current sheets. In a quasi-stationary situation, it balances the reconnection rate, which turns out to be much lower than in guide-field approaches. Another important consequence of the obliqueness is the field-parallel emission of runaway electrons. Accelerated up to tens of keV, they are possibly important contributors to the production of hard X-rays during the impulsive phase of a flare, but only in areas of upward-directed currents. Quantitative evaluation of the model predicts various potentially observable properties, such as width and propagation speed of the generated flare ribbons, spatial dependences of the electron spectrum, size of the area of energy deposition, and successive decrease of the shear angle between conjugate footpoints. The presented theoretical model can account for the observed brightness asymmetry of flare ribbons with respect to the direction of the vertical currents. [ABSTRACT FROM AUTHOR]