I simply do not wish to kill Gerolt (this time) since I'm playing a "good guy" and killing that sad old woman is not in his character...so are there any alternatives in order to meet Astrid in that abandoned shack?

Nope, don't think so. Just do this: Kill. You will feel horrible about it. You decide to go out and do some fun things, and keep saying to yourself: I had too! It wasn't my choice!

Are you really so afraid to get your hands dirty? Noone is pure good, or pure evil.

Use a fury spell on one of the kids.... that way it wasnt you who killed her.

She isnt a sad old woman, she is a horrible [censored] who gets off on child cruelty, the way she treats them is against the law, and jail is not good enough for a criminal of that calliber, she underfeeds them, makes them labor, in my eyes that is slavery... My character is a good guy, and her death was only slightly on his conscience, but when he came back and found out how the kids were so much better off with Constance as their gaurdian, it made me feel much better... anyway, the old hargraven had a few cruel years left at best, a few years of child torment was something i could not let happen..

Well, I usually play a "good guy" aswell, who will uphold the law, protect the innocent
and liberate people from oppression. I have killed Grelod the Kind in almost every
playthrough!

She's a menace to society, an oppressor, an "evil" human being. Killing her won't hurt
anybody, and she is directly responsible for her own fate. The orphaned kids will have
a better life under the care of Grelod's assistance, Constance Michel. You're basically
doing everyone a favour, although Grelod may not be the worst of the worst.

It would basically be like killing a child rapist who has traumatised a kid for life, before
he did it. These kids would probably never have a chance of leading an ordinary life
under the cruel hands of Grelod the Kind.

I'm against death penalty myself, but this is not real life - this is Nirn.

This.

Think of it this way: you're helping some poor orphan kids. It was an abusive situation.

Hmmm alright then, although I wish there were other options, like kicking her out.