There is no method to convert all shapes to inlineshapes in a single action. That said, try:
Code:
Sub Test()
Application.ScreenUpdating = False
Dim oSec As Section, oHftr As HeaderFooter, s As Long
For Each oSec In ActiveDocument.Sections
For Each oHftr In oSec.Headers
With oHftr
If .Exists Then
On Error Resume Next
For s = .Shapes.Count To 1 Step -1
.Shapes(s).ConvertToInlineShape
Next
On Error GoTo 0
End If
End With
Next
Next
Application.ScreenUpdating = True
End Sub
Do note that, when you convert shapes to inlineshapes, there is no guarantee they will end up in their original positions. Rectifying that would require a considerable coding effort.