Awww I love that fuzzy stage, so darn cute (the hardest stage for me to feed off to be totally honest).

With mice and the african soft furred rats, I wouldn't be touching any babies but my regular rats I'm never worried about. Most of my breeding female rats are pretty tame all in all and I've yet to have a mother rat reject babies due to my smell on them. I actually try to seperate every mom from her litter within the first 24 to 48 hours and get a quick hands on look at each pink just to make sure they are feeding well (obvious milkbands) and there are no physical deformities.

The only issue with that is to watch that momma rat isn't a bit nippy. Even the most even tempered rat can be different when she's got a litter nursing so I'm careful of that just in case.