Is there a confirmed historic record of using "non-standard" live animals for military purposes?

Togakushi Daisuke during the battle of the Kurikara Pass placed torches on cattle and directed them at camped Heike soldiers which panicked them into retreat and some ten thousand killed themselves as they fell from Kurikara Pass. My reference is Ninja Attack by Hiroko Yoda.

It pains me to think about but during World War 2 Russia used dogs carrying bombs to seek out tanks and armored vehicles. Training typically involved starving the animals and only feeding them...underneath tanks and armored vehicles. The United States dedicated resources to a similar program but for use against static fortifications, also during WW2. Bomb dogs were last seen in the 2000's during the Iraqi resistance to U.S. occupation, in addition to bomb donkeys.

The original idea was to have the dog drop it's explosive payload and return to its handler. Two problems; remotely detonating explosives requires timers, or remote detonators, which fall into the categories of 'unreliable' or 'expensive', and sometimes the dog returned to its handler during training without dropping it's payload. Bad for the dog, bad for the handler. The result- canine suicide bombers.

https://en.wikipedia.org/wiki/Anti-tank_dog

These dogs make a brief appearance in David Benioff's excellent work of fiction "City of Thieves"

The War-Pig has a long and notable history, used primarily by the ancient Greeks and Romans as a countermeasure against war elephants. Some models were incendiary - the besieged would light pigs on fire, aim them at enemy elephant formations, and let them run free.

During the Second Punic War, when Hannibal was trapped by Fabius Maximus, he had torches tied to cows, put out all other lights and drove them towards the area between the main army of Fabius and the troops that he had guarding a pass. Fabius feared a plot and was afraid to move, while his troops at the pass thought the cows were soldiers and went to attack them, leaving the pass open for Hannibal to take. (sources: Polybius, Appian, Livius)

Many years later, when Hannibal was fighting for Prusias of Bithynia, he fought a naval battle against Eumenes of Pergamum in which his fleet was inferior both in numbers and in ability. He therefore sought poisonous snakes, put them in earthen vessels and had his troops throw them onto the ships of the enemy. Eumenes' troops were surprised at this move and had no idea how to deal with it, so they withdrew. (source: Cornelius Nepos)

Caracalla, when attacking the Parthians, apparently employed wild beasts in battle. However, as far as I'm aware, this is only attested by the very dubious Historia Augusta that is known to contain a substantial amount of fiction.

During the 1944 Italian campaign, most notably battle of Monte Cassino, a brown bear was used by soldiers of the Polish 2nd Corps to transfer ammunition.

Wojtek (soldier bear)

During the second Israeli-Lebanon war in 2006, one Israeli brigade used llamas. However, the IDF are considering releasing their stocks of Oryxes,Llamas and Barbary sheep who have been faithfully serving Israel for some years.

Llamas have advantages over mules for cross country work but have difficulty in terraced terrain. They don't like big steps. The antelopes will stay as their skills in brush clearance make them appreciated. Apparently , veterinary care is the main driving factor here. Antelopes are low maintenance whilst llamas are not, with dental work being quite costly.

Near the end of the Viking Age, Harald Hardrada is said to have caught birds that nested in the cities they seiged, attach burning embers to them, and have they fly back to their nests.

The Viking “Air Force”: How Norway’s King Harald Copied Russia’s Queen Olga

So now Harald thought up a scheme: he told his bird–catchers to catch the small birds that nested within the town and flew out to the woods each day in search of food. Harald had small shavings of fir tied to the backs of the birds, and then he smeared the shavings with wax and sulphur and set fire to them. As soon as the birds were released they all flew straight home to their young in their nests in the town; the nests were under the eaves of the roofs, which were thatched with reeds or straw. The thatched roofs caught fire from the birds, and although each bird could only carry a tiny flame, it quickly became a great fire; a host of birds set roofs alight all over the town. One house after another caught fire, and soon the whole town was ablaze.

The Viking “Air Force”: How Norway’s King Harald Copied Russia’s Queen Olga
(norwegiansocietyoftexas.com pg 3)

QUOTING: Chapter 6 of Snorri Sturluson’s King Harald’s Saga: Harald Hardradi of Norway (Penguin Classics, 1966 translation from Sturlusson’s Heimskringla, by Magnus Magnusson & Hermann Pálsson), pages 52–53.

My favorite such use is the missile guidance system developed by BF Skinner (of Skinner box fame) during WW2. It used pigeons. To quote Wikipedia's article on "Project Pigeon":

The control system involved a lens at the front of the missile projecting an image of the target to a screen inside, while a pigeon trained (by operant conditioning) to recognize the target pecked at it. As long as the pecks remained in the center of the screen, the missile would fly straight, but pecks off-center would cause the screen to tilt, which would then, via a connection to the missile's flight controls, cause the missile to change course.

There was one well-known case during the Chilean War of Independence in 1814. Trapped in the city of Rancagua, and outnumbered some eight or ten to one, the Chilean revolutionary, Bernardo O'Higgins rounded up the local farm animals (cows, pigs, chickens) etc., and threw them against the Spanish lines encircling him, using the animals as cannon and musket fodder. In the ensuing confusion, the rebels managed to escape.

Bernardo O'Higgins (Wikipedia)