As ThaLadyPit explained, you can work to manage prey drive but you can't train it out or "control it". The truth is there is an excellent chance your dog and cat may not be able to peacefully co-exist without close supervision. Your pup may be able to manage her drive with the cat but you should never trust your pup around your cat.
I'm not real experienced with E-collars though I know hubs wants to try one with Kaos and I'm not having it. Hubs is a trained k9 trainer/handler for police/corrections dogs and has experience with them. My whole thing is, Kaos is going through a weird secondary fear stage at 10 mos. He has been doing well with his obedience but suddenly is terrified of corrections. The thing is, he responds amazing to me and has always responded well to positive reinforcement. He WANTS to make me happy and with a little guidance to show him what I want from him, he is usually pretty quick to pick it up after being rewarded for his behavior. Hubs is a little more old school and wants to try an e collar with a VERY small correction to see if that works better rather than a correction with a choke, which has caused him to just regress and be more fearful.
Hubs just can't take it that I'm really the Alpha in my house and the dogs listen and behave better for me than for him. Must be a male hormones thing, LOL. That and my Kaos is just a mama's boy.
Anyway, the moral of my long winded story is, I would work the old fashion way. I know it's like starting all over again, but it more or less is. If it worked the first time, it'll work the second time and should be faster than the first as well. Just my 2 cents!