Hello @NPi,
Welcome to SimpleITK / ITK!
First the “bad” news, SimpleITK does not provide support for point set to point set registration (for point data, only the rigid/affine paired point case is currently supported).
ITK does support point set registration, see the PointSetToPointSetRegistrationMethod, and relevant discussion found here.
If your data are intrinsically point sets you might consider looking at tools that only focus on points such as the Point Cloud Library (PCL).
Finally, if you have the time and want to learn SimpleITK in an organized fashion, try the online tutorial.