This is how I do skin to skin after births (with mother's consent):
When baby is born, I have a warm blanket on mom's belly/chest. I use that warm blanket to wipe off the birth secretions. Then I remove the wet blanket and place baby skin to skin between the mother's breasts. Then I take 1-2 more warm blankets and put them over baby and mom. Baby also gets a knitted hat to conserve heat loss.
Mom keeps baby on her chest as long as she wants then! I do all vital signs, assessments, cord clamping, ID bracelets, while mom has baby on her chest. I also make sure that the ambient room temperature is in the 70's, so neither mom nor baby get chilled.
I can also do baby footprints while baby is skin to skin (although, I can get messy doing it). The only time that a "normal" baby after delivery (no resuscitation needed) needs to be off of mom's chest, is when I do the baby's weight and length. I let the mom tell me when she's ready for baby to be weighed and measured.
Eye drops are done right before we go to postpartum, around 1 to 1 1/2 hrs of age.
This initial and prolonged skin to skin contact keeps the baby warm, blood sugars stable, and helps promote early breastfeeding. You'd be amazed at how many babies go right for the breast within 10-15 minutes!