D.S.
I have a non-drop-side crib (Infinity by Baby's Dream) and, if you can believe it, I'm 4' 10". I've never had a problem with it even with a torn rotator cuff in my right shoulder.
When my son was a baby, the mattress was high enough that I could reach in easily. As he got older and we lowered the mattress, he began to stand at the rail when I came in to get him out. Putting him in isn't a problem either. I swing him over the side and set him down on the mattress standing, then lean over to lay him down. That way, there's never any danger of me falling over or dropping him.
I wouldn't feel safe on a step stool because I'd be afraid of falling off it while getting the baby out. But maybe I'm just clumsy ...