If you can, get a list from the airline on just what you can carry on the plane so you don't run into last minute problems. This is often available on their web site.
Last year I travelled with some "lap work". I followed what was on their list and had no problems. For instance, my scissors were small and blunt tipped. I carried only a few needles, only what I needed. I had my embroidery on a hoop, which was fine. I selected the colors I was going to use on the plane, and packed the rest. My whole "kit" was pared down to the bare essentials of what I needed. I know another lady who didn't even take a pair of scissors. She just used an empty floss container to cut her thread. What makes this easy is that it's easy for them to go through -- the less the better for checking over -- and just try to think like they do. What do you have that could be used as a weapon? And then find a substitute.
I'm not a hand appliquer, so I'm not sure what you mean by "something that could hold the block". If it could be an embroidery hoop, then you're fine. If not, then perhaps someone else could answer that question.
Happy travelling!