Your best bet is to set the Application.DisplayAlerts property to False. That is, assuming that your Excel.Application object variable is named "xlApp", all you'd have to do is the following:
xlApp.DisplayAlerts = false;
Note that this will cause the default response to be taken for each dialog box, which is normally what you would want. (There's no good way around this. Leaving DisplayAlerts = True and using SendKeys might be your only other option, but would be ugly and very error prone.)
Since you are making this call via OLE Automation, this call is cross-process, and, therefore, the DisplayAlerts setting will persist until you change it. (If called in-process, via VBA, it is switches back to to true automatically when the routine completes. The same behavior probably applies for a VB.NET or C# add-in called via a CommandBar or Ribbon control, but one would need to test to be certain.)