The Sharafutdinov's retraction is defined for Open Manifolds of Nonnegative Curvature, for example in $\S 3.4$ of the book "Metric Foliations and Curvature" by Gromoll and Walschap.
For Alexandrov spaces, Perelman gave a constraction in $\S 6$ of his preprint "ALEXANDROV'S SPACES WITH CURVATURES BOUNDED FROM BELOW II". But the construction is not "that" rigous compare with the one given by Gromoll and Walschap. He definitly is a great mathematician, but I just want to make sure this is a correct construction. So are therey any published paper or more detailed construction available?