You can totally do this. DH and I spent three weeks in Greece with just a carryon/backpack (a small rolling suitcase that turns into a backpack) each and had absolutely no problems. It helps enormously that you're going to a warm weather place.
-Take small toiletries only (obviously, you have to for the TSA rules anyway). Don't bring shampoo, etc, as you'll get that at the hotel.
-If you can afford it, run down to REI or a travel store and buy a pair of the shorts and shirts that are designed for quick travel washing-that dry fast and don't need ironing. Same with underwear. Wash clothes in your sink (shampoo works great); don't waste time going to the hotel laundry. If it's hot, they'll dry fast. If it's super hot, they can dry while you wear them.
-you only need two pairs of pants/shorts, a swimming suits, a couple pairs of underwear, a couple shirts, a hat, and something warmer. You could buy a shirt and a sweatshirt there, if you'd like. Buy sunscreen there (and a hat if you want one as a souvenir).
-You can get those microfiber towels that roll up small and dry super fast (and I'm curious about workshop you're going to that needs a towel!).
-travelsmith is a great catalogue for travel items. I have one of those dresses that is lightweight cotton, dries wrinkle free, has a zip pocket-can dress up or down. It's awesome.