There are no real customizeable views in the Timesheets application. They will only show projects from which you have tasks assigned to you - for the window of time that the timesheet is set to display. This would include all project types so long as tasks from within them are assigned to you.
The only option you may have (assuming that this is allowed in your enterprise) is to instead create a view in the Task application that filters in only those project types that you care about, and then conduct your updates from the actions button associated with each task. This may be a little more cumbersome depending on your own personal work preference.