I agree with the other couple of posters above who said that you'd be fine just adding the drip system. The amount of ammonia you have in your well water will be handled just fine with your normal biological filtration way before it built up to levels high enough to be a problem for your fish.
Say you drip even 10 gallons a day into your tank. Since I don't know the size of your tank, I'll assume you have a 55 gallon. Subtract substrate, rocks, decorations, evaporation, and fish and you're left with probably about 40-45 gallons of water actually in the tank. That means that, even if your bio-bacteria were on strike all day, you'd have less than .15 ppm of ammonia in your tank by the end of the day. The amount in your water is far less than the amount created by your fish daily. Your bio-filtration will adjust to it just fine.