I agree. Unless you have tons of aiptasia, you wouldn't need the Berghia. Manual methods mentioned above will do wonders.
I understand you want to stay away from chemical solutions, but the lemon juice/kalkwasser methods are natural methods. They work effectively and as long as you use them in controlled doses it won't cause any harm to your tank. However, i must say that if you have tons of these aiptasia i would recommend spacing out the doses you use. Only kill a few a day if you have a decent amount of them. You don't want to kill a lot of them in one shot otherwise your water chemistry could take a turn on you.
I'm sure others would recommend a Berghia nudi, but the problem is, after they have devoured all of the aiptasia, they no longer have a food source and it could be a real pain to try and relocate them to a better home, let alone removing them from your tank. Only use the Berghia if it's your last hope.
Just my opinion of course.