I'm so sorry you are in this predicament! I wouldn't be comfortable with a trainer that believes that choke collars are the only way to train. Personally I believe that positive reinforcement encourages a positive bond and lets a dog use their brain to figure out what we want - not what we don't want. I use an easy walk harness made by the same maker as the gentle lead. I love the easy walk because it hooks in the front and doesn't encourage sled dog pulling like a regular harness but still fastens across their chest and doesn't put pressure on the trachea. The gentle leader is a head harness. I'm not sure how the fitting would be on such a small dog with a small nose. Here's an article on fitting one.
http://www.gentleleader.com/App_Cont...structions.pdf
My bigger concern would be what the trainer is going to expect you to do in training. I think I would talk to them and see if you can't get your money back. Tell them that this isn't a training method you believe in and you can't do it with your dogs. This really concerns me!