On error goto

Maybe like this?

Private Sub runTxShuttleScript(scriptName As String, xlFile As String, sheetName As String, startRow As String, numRows As String, Optional logColumn As String)
    On Error Resume Next

    programm = "c:\program files\winshuttle\txshuttle\txshuttle.exe"
    out = Shell(programm & " " & scriptName & xlFile & sheetName & startRow & numRows & logColumn, vbNormalFocus)
    If Err.Number = 0 Then Exit Sub

    programm = "C:\Program Files\Winshuttle\transactionSHUTTLE8\txshuttle.exe"
    out = Shell(programm & " " & scriptName & xlFile & sheetName & startRow & numRows & logColumn, vbNormalFocus)
    If Err.Number = 0 Then Exit Sub

    programm = "c:\program files\winshuttle\runshuttle8\txrunner.exe"
    out = Shell(programm & " " & scriptName & xlFile & sheetName & startRow & numRows & logColumn, vbNormalFocus)
    If Err.Number = 0 Then Exit Sub

    MsgBox "This operation can only be run on a computer with XXXXX." & vbNewLine & "You do not have the correct software.", _
           vbOKOnly, "No Software Found"
    Sheets("Master").Select
End Sub