Consider the minimal time control problem for a single-input control-affine system ẋ = X(x) + u1Y1(x) in Rn, where the scalar control u1(·) satisfies the constraint lu1(·)l ≤. 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 ε > 0 small, we consider the minimal time problem for the control system ẋ = X(x) + u1εY1(x) + εΣi=2m uiεYi(x), where the scalar controls uiε(·), i = 1,... , m, with m ≥ 2, satisfy the constraint Σi=1m uiε(uiε(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.