I use Bob Smith Industries cyanoacrylate glues. The nozzles screw on to the bottle, and as thus are removable. Maybe Zap-a-Gap does, too?
If the nozzle gets some glue on it during use, try and wipe it off with an old business card or other thin piece of cardboard that you can partially wrap around the nozzle. Don't use paper towels or Kleenex's - they just make a hardened mess. Keep the tip open with a pin or other sharp object. Never snap the cap on until you've done this.
Regardless, the nozzles will sooner or later get a build up of gunk that makes it a little difficult to work with. If so, remove the nozzle and throw it (and the nozzle cap if necessary) in a glass jar with some acetone in it. Screw the metal lid on to prevent evaporation. Lightly shake and swirl jar around a few times to help the acetone penetrate. The acetone will dissolve the CA, and return the nozzle to like-new (or almost so) condition. Although 10 minutes or so will usually do the trick, I've let nozzles and caps soak for days on end with no adverse affects on them.
It's handy to have a few extra nozzles and caps. Sometimes the dealer will stock them. Also, when your bottle is used up and/or done for, keep the nozzle and cap for a spare before pitching the bottle. You can start building your own supply of extras that way.
Hope this helps. I used a fair amount of CA glue when I built and flew RC airplanes a few decades ago. 
