must?
I just want to start the purge dark brotherhood guild quest.

any subtle way to do it without tainting my/follower hand?

No, she's a [censored] though, so you're doing a good thing. If you don't believe me, check the room next door to her bedroom. Its for hanging little chillun up by their hands...(I wish i could have one of those in Breezehome )

Tell your follower to do it? Edit: bah you said no follower too.

Does a conjured killer count as a kill for the player? You could give her a Sanguine Rose.

ok, i take it's a must.

anyway, i did used fire rune, wait for her to step on, close the door, then step somewhere else, waiting for the kaboom

but her assistance does recognized me as the killer "oh plz, plz stop, i yield...."

Yeah, whatever you do, the assistent will keep on recognizing you somehow. :/ I "disguised" myself in Thalmor robes, used a Potion of the Phantom i got from another quest, and acted like I was a Thalmor ghost out for revenge. Of course, it's only in my own mind, but I've tried multiple things to stop her from recognizing me beforehand, but nothing works. I dislike the fact how you still can't disguise yourself with specific clothes, so the npcs will think you belong to a certain faction. It only kinda works during the quest in the Thalmor embassy.

Anyway, I don't believe there's really a "good" way to get to Astrid. You've got to kill someone to get her attention after all. I figured it'd be better for the kids' future to erase Grelod from their lives. Although they like the Dark Brotherhood a bit too much to my liking now ... Well, it's not all that bad, the DB is having some difficulties, with their leader being killed, and the killer leaving her clothes and a warning sign in their very headquarters ...

She's as mean as the Dark Brotherhood. Go ahead. it doesn't count as a murder, if you're worried about that counter in the stats page. Wait till night (2-3 a.m.) sneak in, kill her in the sleep. She will cry, children will go around her bed (it's scripted) but you won't get any bounty.

If you think to talk some sense into Grelod before hand, she'll be so waspish that you may off her there and then! Besides, the youngsters will be so pleased, you'll feel like hero. Constance will lose her head, but in time she'll calm down.

Kill her. She's a nasty piece of work.
You'd kill her even if you were'nt going to join the Dark Brotherhood. Just to save the children.
You don't get a bounty even if you charge in and kill her in full view.
It does'nt count as murder.

Yup that is what I have done. I have no intention of joining the DB with this character.

I killed her while she slept, no bounty for me and the wee ones are happy.

I stumbled upon the orphanage well before I met Arentino, I mentally marked that woman and thought to myself, I'm gonna come back here and kill you one of these days. My character is not a bad guy, but she was just awful. I jumped at the chance to kill her later, DB or not. Then I killed the DB for kidnapping me.

What I do is make sure Grelod is unarmed and place a little frenzy poison into her system. Then I go invisible and watch her try and pummel Constance, who reacts in self defense.

Not as satisfying as taking Grelod's head off myself, but it's a fun little scene.

Just walk into the orphanage and listen to her berate the children. That's enough. Look around and see her torture chamber. Seek out the child in Windhelm. "The Kind" is sarcasm. She's a hag, and that's being kind. I just did the old sneak attack and slit her throat. Constance was terrified, but the kids all cheered. No bounty. Constance just asked me to leave. So I did. And thus Sonja's criminal career restarted.

Yeah, I had no problem with killing her. But people in other towns will worry about "those poor children" after the murder.

There are a couple of times in the game where I wish there was a peaceful way to be rid of a character, but you are forced to kill em'. It's one of the few things about Skyrim I don't like.