Ignoring the class fluff, the Paladin really has everything you want for a Spellsword, in my opinion. If the various smite spells were changed into a proper class feature (and rebranded as "Strikes") and there were good alternatives to the more Paladin-y features such as Lay on Hands, Divine Health, etc., well that's really all you need.
I love the idea of playing a hybrid caster/fighter, as my many hours with Skyrim can attest. I wonder if part of the problem with a Spellsword is that, besides people not being able to agree on a name, it's feels like a concept that works best in a classless system.
Another problem is the lack of fluff. What makes a Spellsword tick, really? What's the obvious fantasy character to base it on? The closest archetypes I can think of are the generic anime protagonists that are so ubiquitous nowadays; the Hero, or the Gary Sue, to be less charitable.