If you have had a baby recently, you might be familiar with the Nose Frida. It is basically a flexible straw that helps you suck the mucus out of your baby's nose without it going in your mouth.
There is a version of this for puppies that works especially well for more liquid mucus. A Delee Mucus Trap is a great tool to help clear fluid in a neonate just after birth. I have to credit this product discovery to Dr. Marty Greer as well, she is so knowledgeable and helpful. I really count my lucky stars I was able to listen to her speak. I can't wait to try out this fully-sanitizable product soon.