Hmm. Maybe to hold true to some of the typical aspects of a khajiit, implement daggers into your close-combat gameplay. Here are some perks/enchantments/techniques I think would serve you in a unique/fun way.
Armor - For a battlemage Ebony has always felt right for me. Pretty much any headgear goes with it since black is an easy-to-match color and/or non-color. Perhaps a mage hood? You could go down the old smithing route if you want a great armor rating. If you want light armor, I guess you could try dragonscale, or if you have the Dawnguard DLC, Ancient Falmer Armor could look cool.
Enchantments - This can get boring quickly, but you could reduce the cost of destruction by 100% on your headgear, ring, necklace, and armor (25% for each piece of equipment, of course) and the remaining enchantments to your taste. Maybe for your leftover enchantments you could add some health boosts, magicka boosts for remaining spell trees, or restoration reduction (Although free restoration becomes admittedly boring).
For close-combat, as I mentioned earlier, you could use dual daggers imbued with a paralysis enchantment, and then proceed to blast destruction magic at your paralyzed foes. Or if you're aiming for a more sword-and-shield type build, you could include alteration and blast a paralysis spell at your opponent, then rush in and hit them while they're down.
Not sure if this counts as a battlemage, but you could go for an armored tank type as well. For this I would recommend Smithing, Heavy Armor, Restoration, Conjuration, Enchanting, and Block. I tried it once and was having massive amounts of fun shield charging my enemies, summoning Dremora Lords, and throwing my shield up in purely defensive manner without taking any direct part in the fight.
Here are some loosely recommended perks that I think serve a battlemage well depending on the path you want to go down.
Block - Shield Wall, Power Bash, Deadly Bash, Disarming Bash, Shield Charge, Deflect Arrows, Elemental Protection (For the mage tank)
Restoration - Respite, Regeneration, Adept Restoration (If you don't plan on reducing the cost 100%)
Conjuration - Summoner, Atromancy,Elemental Potency, Twin Souls (Two is better than one)
Destruction - Augmented Fire, Augmented Frost, Augmented Shock, Destruction Dual Casting, Impact (My Favorite!)
Alteration - Magic Resistance (3/3) is pretty good, seeing as it's an all-around perk, and Atronach (Absorb 30% of the magicka of any spells that hit you) WARNING: Your conjuration spells will fail often if you have this perk. Not sure why.
One Handed -Armsman, Dual Flurry (If you want to go for a dual dagger build), Fighting stance, Savage strike
So sorry if I said too much!