I have access to quite a lot of animals, since I work at a zoo. However, none of them would really be ideal in a combat situation, as we're a small zoo and don't have larger predatory animals like big cats. I could always travel to zoos that do have them, but I still wouldn't be able to stroke a Tiger without risking serious injury, even if I could somehow sneak into the enclosures.
Including the animals I work with, domesticated animals and animals at other locations I could easily get access to:
Dog, cat, hamster, mouse, rat, chipmunk, squirrel, rabbit, guinea pig, horse, cow, sheep, pig, reindeer, goat, variety of birds (including certain birds of prey and owls), variety of small fish, frog, toad, snake (non-venomous), tarantula, scorpion, salamander, skink, green anole, snail (regular and giant), locust, stick insect, ****roach, fly, ant, caterpillar, butterfly, terrapin, praying mantis, assassin bug, lemur, giraffe, emu, wallaby, meerkat, monkey, iguana, chameleon, etc.
I might be forgetting a few. Like I said, most of the animals I work with are small. The only battle worthy animal I could get access to without serious risk would probably be a rhino. They have them at a zoo not far from here and I could probably reach out and touch one without entering the enclosure.