The closest thing to a Paladin in the two latest ES games are the crusaders true, but they aren't holy warriors, just random goodie two-shoes.
Crusaders in fantasy are usually knights who go on quests to find holy relics from their deity, and who of course spread the word of their deity and live by their guidelines. And that is exactly what they are in The Elder Scrolls. However, as far as I know Knights of the Nine is the only storyline where you can see that. But all the knights there are crusaders, and the hero eventually becomes the Divine Crusader...
Point is, the Crusader really is a holy warrior. But of course, you can name yourself a Paladin if you want.
In reply to the OP:
You have chosen 7 skills for the builds of your paladin types. Why not choose 18 instead? Gives you a lot more options.
I mean, in actual gameplay there is no difference between a battlemage and a paladin. What characterizes a paladin is how you roleplay him. So just play the game the way it's intended: Go out there, find out which type of combat etc. works for you, and then focus on roleplaying that character. And if you later find out that you'd rather use 2-H weapons instead of 1-H, then change it. There's no need to have the perfect character right from the start, and even for paladins it's the imperfections that make them interesting.
In your post, you're concerning yourself with thoughts like "is Smithing really something a paladin would do?". Why don't you just find out? Maybe you'll roleplay a paladin who's sworn not to return to civilization before his current quest has ended, and you'll find yourself using a lot of repair hammers because of that. If so, then that's fine.
tl;dr: You guys need to trust the new system more, which doesn't
have builds anymore. You just play and see what character comes out of it.