I know you said that you were concerned about wheeled luggage, but I like this set because of the separate computer/electronics section. You can get them via Vipon for $50. https://www.amazon.com/Coolife-Lugga.../dp/B07114YT17

I don't think you'll have a problem doing a carry-on for 10 days. Maybe just plan for a hotel that offers laundry facilities half way through your trip. We usually try to choose an apartment for at least one night so that we can wash clothes.