Welcome to FT. If you want to take your dog as carry-on, you're not going to find a hard-sided nuts-and-bolts carrier that will fit underseat. You will find either something with snaps or will need a soft-sided carrier.

I fly once a year with my Pomeranian and my chihuahua. I strongly recommend a soft-sided carrier like a Sherpa (or, like I have, a no-name replica). The soft-sided carrier allows you to use a slightly larger carrier and still fit underseat, and makes it more comfortable for the pet to stand up and turn around.

The airlines don't care at all about the locking mechanism, in my experience. However, as I said, for in-cabin travel I would strongly recommend a soft-sided carrier instead. If you're checking the pet to be shipped as luggage, then a hard-sided carrier with secure locking mechanisms is required.