Newborn & step children

Okay so I'm due in a week and I'm freaking out. My partner and I have been together for 13 months. He has two children both under 6. When they visit they always seem sick. Runny noses, cough. All that fun stuff, I'm a bit of a germaphobe and my partner hates it. I don't know how to tell him that I don't want the kids kissing the new born or even handling her. Especially for the first 6 weeks until she gets her first shot.  They never seem to wash their hands after the toilet and they never listen to me. I feel like a horrible person because she's their sister too but I don't want to risk my baby getting sick especially seeing it's winter where I am.