About the reactor itself, should air pass directly in contact of the hot fuel? or with a primary coolant system? It will completely change the type of reactor you need, the neutronic moderator, the type of fuel, his size.
If you want to go small size, submarine type reactor (Pressurised Water Reactor and Fast Neutron Reactor) are good, but you will have weight problem (primary coolant system are heavy, several tons of water, lead, pumps...). With gas cooled reactor you will be bigger, but a bit less heavy.
In the case of air going directly on the nuclear fuel... forget it, no sane country will allow a system like this flying above them, it will spread contamination all around.