Sorry for the delay, brneyes. I was away for the weekend and just returned.
There are two types of trash ties I'll use for luggage. One is the simple twist tie -- the very thin wire covered with paper or pliable plastic. These are the easiest to use as there's no need to cut anything. Twist them on, twist them off.
The other type is the pull-tie that often comes with lawn-and-leaf bags. There are pre-cut holes in them, and you just put one end through the holes and pull tight. These are more difficult as you do need a small pair of scissors or something else with which to cut them. I will do one or two things in this case -- either pack a small pair of scissors in an unlocked (or twist-tied) pocket of a checked bag, or ask for a pair of scissors at the hotel desk when I reach my destination.
Shelby, I do suggest securing your bags somehow, either through locking or the trash-tie method. I use the twist ties mainly as a way of deterrent -- it takes a bit of time to "untwist" the twist ties... the person might instead just move on to the next bag...