Hi A. -
When your son puts his hands in his mouth, all you can think of is, "GERMS" --- put that thought aside for a minute and think past it. It is blocking you from what is really going on.
Now, there are many things you can rule out -
Has he been to a dentist yet? He could have something going on with his teeth, like swelling, a cavity that is hurting him, or an infection, even a yeast/thrush problem which makes his mouth itch - very common. Also, if he has allergies to any foods, his mouth will itch, or from reactions to acidic fruits, etc... his mouth will itch. Any seasonal allergies can also cause this problem. Remember that at age three, kids certainly cannot always put into words what is bothering them. And, this is why you have to think outside the germ box.
Secondly, there are some children that are very oral - they keep doing this - putting their hands in their mouths or objects in their mouths at even the age of three. These children are still building nural connections and are usually highly intelligent kids - it's just the way they are wired and it is literally a biological need they have to do this.
Remember too, that he is still building his immune system and unfortunately this strengthens it - germs. Our society is germ-phobic and I can attest to being a germ-phobic mom. However, there are so many "good germs" in the sense of what we need to build and protect our bodies.
I know it is hard, but don't let your considerations cease at the thought of germs, germs, germs. For your little boy's sake, you have to get beyond this and figure out what is really going on. If you don't, you are letting the issue with germs rule over possible needs your child has and I am sure when you see things in this perspective, you would not want to do that. Have you asked him questions about his mouth, or his hands? Have you thought to have him color a picture of how he feels with his hands in his mouth? These are tools to use with small children that still lack more clear communication skills. Get creative and try and see what is behind this.
Good Luck A. - I know you'll figure this out. Also you can ask if you or your husband had a similar tendency when you were both children.