I know some trainers shy away from using a harness because they feel that it can cause the dog to pull more on the lead. Of course, if you train your dog not to pull from the time it is as young as yours, you probably wont have a problem like that. Plus, there are some no-pull harnesses available to help reduce the problem if you end up with a naturally wanna-pull dog.
If you still have the meeting with the trainer, it might be helpful to print some of the documentation about SM from the site. So that, when he explains to you why you need to use a collar, you can explain why you need to use a harness. If the trainer is unpersuaded by your scientific reasoning, you can let the trainer know that this is a make or break issue in hiring him, thank him for his time, and that you will find a different way.
The puppy trainer I assist in my club advises against harnesses, and then after the class I quietly make may way over to the small dog owner whose dog is in a harness and tell them that, if they want to use a harness, I've done it and can lend advice. It's doable, and if you go to the expense of hiring a private trainer, they should be able to accomodate.
Cedar (tri), Willow (blen), & Holly (ruby)