Pretty sure there’s a shorter path to the top of the intestines than through the nose but I’m no Biologist.

If you’re implying it is through the rectum, you’ve definitely got some bio to brush up on. The small intestine alone is >20ft long.

There really isn't. From the mouth is basically the same distance and it contains teeth and a tongue. Through the rectum is much much much farther through meters of intestine. Through the skin creates a surgical hole that's going to be difficult to keep sterile.

The shortest safe path is via the nostril.