One of the ladies at the market I attend uses matchsticks (with the heads cut off) dipped in the lip balm and has them standing in a piece of wood with holes drilled into it. I've never seen it done that way before but thought it quite clever.
I have a little pot of each flavor and little spatulas they can scoop out with to try if they so desire. All my other tubes are sealed. In all the years I’ve been doing its Worked well. I also have a sign that says no fingers
I keep sample of my lip balms behind in a small container behind my display. If someone is looking at lip balm I ask if they would like a sample. If they say yes I give them the sample using clean mini birchwood sample sticks I keep in a covered plastic container that no one touches using a mini appetizer tong to pick up the stick.
I go back and forth with offering lip balm samples, and not offering. I seem to get more interest when people can smell the lip balm, but I'm not sure that actually turns into more purchases. When I do offer samples, it's as everyone mentions above - an open tube with a small wooden stick. The open tube gets tossed at the end of the show (if not before - because someone always puts it super close to their face or uses a finger). I'm really leaning toward not offering "testers" anymore.
It just is not difficult to control the sample. My customers see me remove the sample tube from the enclosed case and the samples from their box. It almost always gets the sale. Just a little personal touch. I have also sprayed my hands with alcohol before getting the samples. Just a leftover from my cosmetology days and having a daughter with a low autoimmune system. I will mention that I usually only have lip balms during my Holiday markets because I simply hate making them.
I have been using the little spatula approach, same as @shunt2011 at Farmer's Markets. I like @cmzaha 's approach, may switch to hers.
At the honey bee booth at the state fair, I do not have samples as the booth is manned on a rotating schedule. Of course there, I only have products that have beeswax or honey in them. I sell plenty of balms, but it is a different type of customer/crowd, than the Farmer's Markets. I have sold there for 4 years; now people come to the booth and ask for my lip balm.
I have a display for 12 flavors with room for a sample tubes at the base. There's a small container of flat-headed toothpicks and a tiny stone bowl for discarded tooth-picks. It's right where I stand so I can keep an eye on it and I've never had a person actually try to apply the sample tube to their lips. Some people will smell it, and I mention that toothpicks are there if they want to see how it feels.