A friend of mine like to take hand quilting with her when she travels. She take cuticle scissors for cutting threads with no problem. Because they are curved they cut really close. Great idea for using at home also.

I travel with the small scissors less than 4 inches, needles and thread. I always have them out in a small zipper case so when you go through security they can see what they are and you are not trying to hide anything.

I have a pair of Gingher embroidery scissors with the rounded tips. They have been with me where ever I fly. You can also pick up a little thread snip in most notion areas of fabric stores. They usually are round but may be in the shape of a bug or animal. They have a blade in them similar to the cutter on your sewing machine.

http://www.barnyarns.co.uk/madeira-thread-cutter.html

I use this cutter and works like a charm!

I would search the airline and the TSA sites, print their restrictions/recommendations and take that with me so I can prove I checked. I have seen wide variability in what's allowed and if you can show where you checked, it can make a difference in what gets allowed. Sometimes it's subject to individual moods and interpretations!

Thanks all for the wonderful advice! TSA guidelines seem to indicate that embroidery scissors are fine, but, as someone else pointed out, they change the rules so often that I will go armed with a small pair of cuticle or blunt-nosed scissors AND a pair of nail clippers AND some dental floss. They can't stop me!

Check with your airline for the most accurate and up to date information.

It also depends on what country you are flying to. I found out the hard way. My tiny little scissors were fine until I reached Australia. They have their own rules. I had to get out of the security check line, go to the airport Post Office, buy a padded bag and mail them to my daughters home (in Australia). Otherwise they would have confiscated them.
At least I had that option. It cost me $6.50 AU. Money to mail them to her but they were my favorite little scissors and I was going to be using them while there. We do a lot of sewing together. In the USA, TSA rules would have allowed them.

Also check out www.tsa.gov and the website for your departing airport.

To get the most up-to-date and complete answer about what is permitted on a flight, go directly to the airline information office and ask them. That way there will be no guessing and you will know exactly what is permitted and what isn't.