I'm glad you are going to conformation classes with the kennel club. They will help you and you will meet some great people there. 40 miles isn't that far to drive really. Their help will be invaluable. Whether or not they have any experience with chi's, they will have experience with other breeds and structure is structure. (As you probably know from showing horses.)
As long as he has both testicles, there's no reason he couldn't be shown. And you could learn the show ropes with him. (And build points for others! Which they will appreciate.
) It would be embarrassing if he was dismissed by the judge for lack of merit, which does happen. But it will be awhile before you get to that point. You have lots of time to learn in the meantime before you enter your first show.
You might as well give it a go and see if it is something you are interested in. If so, you can then buy a good quality show prospect and be on your way. We all had to start somewhere. Actually training and showing your dog goes a long way in showing a serious show breeder that you are truly willing to learn and then you may be able to purchase a quality dog.
In the meantime, study study study the breed standard and especially the illustrated standard. Go to any and all dog shows you can find. Invest in learning and it will pay off.
This is from the british standard, for example, but you get an idea on how an ideal chihuahua should be built and how to train your eye to look for faults ....
We are not a "head breed" as much as bulldogs are, for example, for the head is very very important. Spend time learning what a correct headpiece looks like, eye placement, ear shape and placement, the stop, the angles between the forehead and muzzle, a correct bite. A beautiful dog with a plain head will not go far. All the pieces of the puzzle must come together. This is called breed 'type'. Over time, you will learn what that is and how it applies to our breed.
You can even go to breeders websites that are currently out and showing their dogs (people active in the breed, not just cutesy puppy selling sites) and study their show photos and stacked pictures of their puppies and dogs. Look at the general appearance, the shape of the head, the set of the ears, the topline (which should be LEVEL), tail set, angulation of front and rear, feet, etc. This will help you develop a critical eye. Along with studying the standard, that should help you learn what is correct for the breed.
Last but not least - make sure you keep an eye on his joints, hips, knees (patellas) as he grows. Have your vet go over him critically for soundness. The most beautiful dog in the world should not win (or reproduce) unless they are totally 100% sound.
Edit: Just want to say to not use Brody as any kind of example of what a quality bred chihuahua should look like.
He is a wonderful pet. But he would never be competitive in shows. Not in the slightest. It doesn't mean we love him any less or that he is worth less than the most titled show dog out there. It is just the truth, he was randomly bred by pet people with no understanding of structure and conformation.