Will a betta fish die if he swallows a hair?

When my betta gets long fibers or hair stuck in his mouth, I put him in a glass bread baking dish with 2" water & net him. I take tweezers and very very slowly pull it out - if it wasn't rectified on its own in 2 days. I put half dose of stress guard in tank and wait 6-8 hours to feed him. They have all survived this. If it stays in the gut & mouth you risk infection. I have a ceiling fan that blows things in tank so I try to keep majority of it covered with air holes.