There are actually a few good reasons never to use a lead on a collar when walking a cavalier or training a cavalier (or any other breed of dog, for that matter).
The reason I would not do this for Cavaliers is that there is such a high incidence of eventual syringomyelia in the breed–at least 70% by the time they are older than 6, according to estimates from a 555 dogs sample. More than one neurologist feels that using a collar just puts pressure on this sensitive area and could potentially risk making syrinxes develop, or make them worse. For dogs that do have the condition, almost always, a collar is extremely uncomfortable (which is why a common early symptom is scratching when on a lead and collar). They suggest a harness is always best.
The reason why I would use a harness anyway, is that every vet I have spoken to says they are preferable for a small breed in particular because they do not put pressure on the trachea and collapsed tracheas are a problem for small breeds.
The reason why you never need to use a collar for training is that it is only necessary if the method of training is the outmoded punishments approach–of jerking the dog around by the collar to “correct” things you don't want the dog to do. Numerous studies have shown that using such methods are at best, counterproductive and can actually cause behavior problems like fear aggression, as well as do physical damage. Cavaliers are a very sweet natured, sensitive breed that are also very food motivated and are so easily trained using positive methods, and are easily made overly fearful by jerking them around on their collars doing “corrections”. I would only look for a class that uses positive methods (e.g., rewards-based methods) in which case it matters not one jot whether a dog is on a collar or harness. I trained all of my dogs on harnesses, including the dogs that do agility, and never had a single issue with having the dog on a harness as opposed to a collar.
All my dogs wear collars because they are handy for keeping their tags, but I don't walk them on the collars.