Let's not confuse the hunting sword, with the gentleman's short sword, or the officer's sword.
They are not the same things, and back in their day, they were recognised as such.
The hunting sword was indeed to dispatch a large, wounded animal. They were originally longer than any butcher knife of their time. Normally they were straight bladed, for thrusting, and the smallest would have a blade of say 17", with many as long as 22"-24". Shorter knives with similar hilts to the hunting swords, appeared in the 19th century and into the 20th century..., these are hunting daggers.
A simple cross guard was all that was normally present on a hunting sword, to prevent the hand from moving forward onto the blade when a thrust was made. Sometimes a chain went from one of the tips of the guard to the pommel. Sometimes the guard was S shaped
The Germans seem to have favored the shell cover/guard for the sheath, and early forms of this sword often had a smaller knife for butchering and skinning the slain animal. The French seem to have employed some hunting swords with a curved blade. They are not very robust and are not similar to a hangar or a saber.
Jaegers in Germany, who were not from the gentry, carried these swords along with their rifles. When serving in the army, as the American riflemen were to carry a 'hawk, the German Jaegers were to carry their hunting swords.
When the AWI began, many American militia officers, and some regular officers, only owned a hunting sword, and so employed those for "officer swords". Some officers carried infantry "hangars". These are not hunting swords, and although they were not carried by privates by the AWI, they were often carried by sergeants as well as officers.
The gentleman's short sword was very different from both the hangar and the hunting sword, with a complicated hilt, and complicated techniques for use for self defense. Extremely quick, and quite deadly, they were thrusting weapons. They were acceptable as an officer's sword. The same hilt with a longer blade was normally the "officer's sword".
LD