Basta ler a primeira linha e descartá-la:
Sub Luxation()
Dim InputFile As String, OutputFile As String, strData As String
InputFile = "C:\TestFolder\File1.txt"
OutputFile = "C:\TestFolder\xxxx.txt"
Open InputFile For Input As #1
Open OutputFile For Output As #2
Line Input #1, strData
Do Until EOF(1)
Line Input #1, strData
Print #2, strData
Loop
Close #1
Close #2
End Sub