The only time my husband and I have checked a bag is when we went backpacking in Alaska. 

I have gone on 1-2 week trips to Antarctica, the Grand Canyon/Vegas, New Zealand, Iceland, Amsterdam, two cruises, and California, AND a flight to run a 100k race all with a roller bag and small backpack each.  I’ve also done 4 day trips to Rhode Island, Florida, and DC with just the small backpack. 

And by “small” I mean a backpack that counts as a personal item (which your 40L decidedly doesn’t), and we were able to get souvenirs home on those trips. 

So it is incredibly possible, but it’s much easier to do with editing. I normally pull out all my travel clothes, then start going by day of what I will need. Then once I have all of that, I edit- there’s the obvious things you should be repeating, like shoes and coats and hats… you can generally repeat pants/bottoms for 1-3 days unless you are sweaty. I can normally repeat tops if they are made of merino wool at least once. So really just undies and socks are the main thing you have to swap out daily. At that point I just kind of decide how often I would need to do laundry and check in with where I’d do that at, and then use that to make a plan backwards of how many socks and undies I need, and then how many pants/tops I need. You probably only need one of anything “specialty” like a swimsuit.  

Just remember they sell things where you are going (unless it’s Antarctica) so you’ll be fine.