This thread baffles me completely.
Your sis has asked to cuddle your newborn, she is going through a difficult time. Your sis has little experience in handling babies and got it wrong once by almost waking your baby up for a cuddle.
If your baby does not want held by your sis your baby will make it perfectly bloody clear. This will probably put your sis off. If your baby is happy with the situation it causes you no pain and your baby gets a lovely cuddle from their auntie.
I really really don't see the problem.
As pp have said, if your sis was crying over your baby 24hrs a day, there would be a problem (and even then not an unfixable one, plenty of babies survive very well with mothers who suffer from PND)
Your feelings about supporting your sis with her depression and counselling however need examining. It seems that you are happy to be a shoulder to cry on as long as it doesn't actually mean you have to put yourself out. Which is great, or its better than nothing. Lots of family members walk away when someone is suffering from depression. So well done on being there for her.
Perhaps, instead of worrying yourself silly over nothing, you could use this time to teach your sis about baby care.....or at least how waking a sleeping baby is not helpful