I use destruction and Archery instead of a sword, would this still make me a Battle-Mage or a Witchhunter. I know classes don't exist but this is for naming my armour for it's purpose.

I would say yes. Loose battle-Mage.... But battlemage nonetheless.

I think witch hunter just because that's how it was classed in Oblivion.

I would say witchhunter but even better if you hunt hagravens and witches

I don't really hunt stuff...

I think witch-Hunter

One is only witchhunter if one hunts witches, daedra, necromancers etc. as an occupation. Just as using an eclectic mix of combat, magic and stealth skills doesn't make one a bard; poetry, music and stories do. Battlemages are mages who study magic almost entirely for combat and they'll also train in back up non-magical techniques which may include archery. They are often military officers and study war tactics as well. Spellswords are essentially warriors of some type who use magic in more or less equal proportion to mundane combat. Calling someone who uses a bow rather than a sword a spellsword is a bit odd, but it may be more appropriate. Think about what your character does as much as how he does it.