Peter's not going anywhere, he may in fact even be using his sticking ability to really stay planted.

"I can't exactly with that one, knowing everything Mr Stark is done-but he's really out of it and if you can't promise not to just let him rest then-I'm really sorry about this." He's gonna regret this. It's gonna come back to bite him in the ass just like the mishap earlier with the lavender death room and pretty much how everything he does in his life tends to do.

But, without another thought beyond 'this is a bad idea' he fires his webs at her, hoping to trap her to the wall directly across.