A 3-week business trip without checking luggage?
I see that list as very reasonable for a carryon. To the previous poster's point, make sure to carry/wear your winter coat and bulkiest items. Domestic or intl I always carryon and the only issue you start to have is adding more shoes that typically take up the most space.
If you're not staying at a hotel with same day laundry and no coin op available, most dry cleaners have 1-2 hr options for usually double the price. Stick to making a carryon work, losing your luggage on one leg could leave you with nothing for 2-3 days.
Oh, and if all else fails you can pick some woolite and wash clothes in your hotel room sink.