Sue, I'm a Paramedic (retired) & First Aid attendant, and always travel with a small First Aid kit. It's quite small and packs easily, and I've had to use it on a couple of occasions. I normally check my large Pack, so haven't had to deal with scissors in carry-on, however I believe the blunt-end models are OK. I carry Advil, antacids and similar med's in my toiletries kit, and that way the FA kit doesn't get overloaded.
I normally start with a basic kit such as this one and then tailor it to my own preferences. I'm sure you could do the same with a kit obtained locally at a Drugstore or whatever.
A small kit won't be suitable for all contingencies. Tailor it to the minor injuries you'll most likely encounter while traveling (cuts, blisters, etc.). At least one Triangular bandage is a good idea, as they're so versatile.
Good luck and happy travels!