I like Zap and have been using it for years, although I am starting to lean in the Tenax direction!
I always put the long, conical applicator thingy on the Zap bottle, and then leave a straight pin in the hole to close it up. Occasionally the pin will glue itself to the bottle, but a pair of tweezers and a tug and it comes out. I know some people who just leave the bottle open and don't have evaporation problems.
Also, I dislike using toothpicks to apply it. It seems that the ones I get always tend to soak up the glue before I get it to where I want it. I usually use a piece of thinly stretched sprue or just a straight pin.
CA is going to be your best choice for PE parts as far as I know. About the only other thing I can think of would be epoxy and that is way too thick and way too much trouble.