Consider the minimal time control problem for a single-input control-affine system (x) over dot = X(x) + u(1)Y(1) (x) in IRn, where the scalar control u(1)(.) satisfies the constraint vertical bar u(1)(.)vertical bar <= 1. When applying a shooting method for solving this kind of optimal control problem, one may encounter numerical problems due to the fact that the shooting function is not smooth whenever the control is bang-bang. In this article we propose the following smoothing procedure. For epsilon > 0 small, we consider the minimal time problem for the control system (x) over dot = X(x) + u(1)(epsilon)Y(1)(x) + epsilon Sigma(m)(i=2) u(i)(epsilon)Y(i) (x), where the scalar controls u(i)(epsilon)(.), i = 1, ... , m, with m >= 2, satisfy the constraint Sigma(epsilon)(i=1) (u(i)(epsilon)(t))(2) <= 1. We prove, under appropriate assumptions, a strong convergence result of the solution of the regularized problem to the solution of the initial problem.