Prueba este código:
Declare Function ShellExecute Lib "shell32.dll" (ByVal hwnd As Integer, _
ByVal lpOperation As String, _
ByVal lpFile As String, _
ByVal lpParameters As String, _
ByVal lpDirectory As String, _
ByVal nShowCmd As Lonf) As Long
Const SW_HIDE As Long = 0
Const SW_SHOWNORMAL As Long = 1
Const SW_SHOWMINIMIZED As Long = 2
Const SW_SHOWMAXIMIZED As Long = 3
Const SW_SHOWNOACTIVATE As Long = 4
Const SW_SHOW As Long = 5
Const SW_MINIMIZE As Long = 6
Const SW_SHOWMINNOACTIVE As Long = 7
Const SW_SHOWNA As Long = 8
Const SW_RESTORE As Long = 9
Const SW_SHOWDEFAULT As Long = 10
Dim X As Long
' Para ejecutar el fichero "C:Mi_pathMi_fichero.exe"
X = ShellExecute(Me.hwnd, "Open", "C:Mi_pathMi_fichero.exe", "", "c:", SW_SHOWNORMAL)
' Si quieres que te lo ejecute minimizado, sustituyes SW_SHOWNORMAL, por SW_SHOWMINIMIZED, etc...
' En realidad la definición de las CONSTantes no es necesaria: sin definirlas podías haber escrito directamente
'X = ShellExecute(Me.hwnd, "Open", "C:Mi_pathMi_fichero.exe", "", "c:", 1)
'pero en este caso no sabrías qué significa ese uno...
Saludos y suerte