I don't think that the Self-Defense Navy would actually be able to stand up to the Khemish Navy one on one and actually be able to hold nonetheless offer a pitched battle. My navy is more focused on defending Keras itself and its control of the straits. Most of its ships would be designed for coastal warfare along the islands of the straits. So I would think something along the lines of the Swedish Navy of World War II. Lots of destroyers and submarines, some cruisers and perhaps four coastal battleships. So the Keran forces would prefer mini-battlegroups designed to harass shipping and to attack isolated ships and garrisons as well as ambush tactics along predictable sealanes. Keras itself would be used as an unsinkable aircraft carrier similar to Malta. I do like the idea of a movable nation of exiles. Most will be either soldiers of the Self-Defense Forces and the Honoured Garde, so I could see while Keras is under occupation, the Free Keran Forces keeping the fight up. And perhaps even a Keran resistance within the city, supplying information, sabotaging the occupiers and collaborators and preparing for an uprising when the Free Kerans arrive.