For a syringe try a livestock feed & supply store, sometimes pet stores have them, and vetinary clinics. Not sure what else you have in your area but that would be a good start.
I haven't had any luck with peppermints of course I can't keep them long term because of my Sally Lightfoot crab, but others have had good luck with them. Even with peppermints I would kill any aiptasia that you can see and let the peppermints take care of the ones you can't see.