You're doing the right thing to put him into the gymnastics class for now, and the way you are thinking of expressing it to him sounds very good.
Don't let him see your own disappointment, though. He will quickly pick up on it and decide he's upset and disappointed too. You may find you feel worse about this than he really does -- kids at 4 sometimes just move on. You may be surprised at how readily he might say "OK, that sounds fine" and carry on. I wouldn't try at this age to shop around and ask schools to take him at four; that would be a lot of work for what sounds like just further disappointment for you, and he'd be aware of it.
He may end up identifying himself as a gymnast rather than, or in addition to, a martial artist. Four is really young for our kids to be fixed on a single activity anyway, so variety is good right now. By age five he may want to do soccer or swimming along with martial arts too -- encourage him to try different things.
As for having dad teach him in the coming year -- maybe some forms etc., but I'd be concerned that if dad taught him a lot, then when your son enters a new martial arts class with other kids at age five, he's doing things that either are more advanced than the class (and gets bored and frustrated) or doing things in a different style from what the class teacher wants (and he'll be constantly corrected and get frustrated). I might let the future teacher do that job and just have dad encouraging him in gymnastics etc. but hold off on too much "teaching" by dad unless he's used to working with and training young kids in his martial art.