I think having a fighting skill, unless it's archery, is pointless with a tamer. Your pet tanks, your pet takes the most damage. Outside of casting spells to do additional damage, most of your attention is focused on healing your pet and keeping your pet alive as it will do the most damage.
I have three tamers. 2 bard tamers, 1 mage tamer. The mage tamer spends a lot of time throwing healing spells and vetting the pet and has only occassions to toss a spell on the creature - like Melissandre if we are 2-3 tag teaming it i'm healing all three pets with magic and healing my own with vet as I go. There'd be no time to fight and keep yourself alive in a fight like that.
I'm not sure how good Chiv is at healing a pet either.