You should be able to ShellExecute the dwg file so it opens with its associated program which is Autocad.
Code:
Option Explicit

Private Declare Function ShellExecute Lib "shell32.dll" Alias "ShellExecuteA" ( _
                    ByVal hwnd As Long, _
                    ByVal lpOperation As String, _
                    ByVal lpFile As String, _
                    ByVal lpParameters As String, _
                    ByVal lpDirectory As String, _
                    ByVal nShowCmd As Long) As Long

Private Const SW_HIDE As Long = 0
Private Const SW_SHOWNORMAL As Long = 1
Private Const SW_SHOWMAXIMIZED As Long = 3
Private Const SW_SHOWMINIMIZED As Long = 2

Private Sub Command1_Click()
    ShellExecute Me.hwnd, "open", "C:\Users\Public\Test1.dwg", vbNullString, "C:\", SW_SHOWNORMAL
End Sub