This is just a guess, since I can not test it yet, but I think that if you truly want the manual user interface dialog to show, specifically for editing an existing feature, then you would have to 'select' that feature, one way or another, then execute the same command as the one in the right-click menu. Below is an example of a code like that, which I have not tested yet.
Sub Main
Dim oDoc As Inventor.Document = ThisDoc.FactoryDocument
If oDoc Is Nothing Then Return
If (Not TypeOf oDoc Is PartDocument) And (Not TypeOf oDoc Is AssemblyDocument) Then Return
Dim oSS As Inventor.SelectSet = oDoc.SelectSet
Dim oCD As Inventor.ControlDefinition = ThisApplication.CommandManager.ControlDefinitions.Item("EditFeatureWrapperCmd")
Dim oFFs As FinishFeatures = oDoc.ComponentDefinition.Features.FinishFeatures
For Each oFF As FinishFeature In oFFs
If oFF.Name = "Face1" Then
oSS.Clear
oSS.Select(oFF)
oCD.Execute
End If
Next
End Sub
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Wesley Crihfield

(Not an Autodesk Employee)