I have written this piece of code, which can start to record the graphics window by prompting the "record screen capture to file" UI. I can end this process by replacing the swCommands_ScreenCaptureAvi_Begin with swCommands_ScreenCaptureAvi_End command which will generate a nice avi file of the part.
Dim swApp As SldWorks.SldWorks
Set swApp = Application.SldWorks
Debug.Print swApp.RunCommand(swCommands_ScreenCaptureAvi_Begin, Empty)
Debug.Print "[Status] Recording"
However I wonder if it is possible to automate this process, by setting fixed parameters for the "record screen capture" UI part which could then be used to start and stop the screen recording without launching the UI. Else if there is any other possible solutions to which you could direct me, it would be appreciated.