No, the Japanese Constitution has nothing to do with aircraft carriers. Or exports of military equipment. Those are government policies, nothing more.
I seem to be posting this about once a year.
Here... read it for yourself.
THE CONSTITUTION OF JAPAN
And the legal interpretation that allows a military that isn't a military:
I. Constitution of Japan and Right of Self-Defense
From the last link:
The self-defense capability to be possessed and maintained by Japan under the Constitution is limited to the minimum necessary for self-defense.
The specific limit has a relative aspect of varying with the international situation, the level of military technology and various other conditions. It is defined in the Diet, the representatives of the people through deliberations about each fiscal year budget etc. However, whether or not the said armed strength corresponds to "war potential" prohibited under paragraph 2 of Article 9 of the Constitution is an issue regarding the total strength that Japan possesses and maintains. Accordingly, whether or not the SDF are allowed to possess some specific armaments is decided by whether the total strength will or will not exceed the constitutional limit by possessing such armaments.
But in any case in Japan, it is unconstitutional to possess what is referred to as offensive weapons that, from their performance, are to be used exclusively for total destruction of other countries, since it immediately exceeds the minimum level necessary for self-defense. For instance, the SDF is not allowed to possess ICBMs, long-range strategic bombers or offensive aircraft carriers.
Defensive aircraft carriers are perfectly OK.