Do they bite? Hell even if they do I probably would do it.
They bite. Loads of "harmless" spiders, including house spiders, bite in theory but seldom in pratice. Most spiders that CAN bite will do so when they're feeling squished or about to get sat on for example - some do it defensively and aggressively.
The problem is that even with tiny fangs, and low venom, that's a lot of potential microdoses and even more problematic - a lot of bacteria and other nasty crap in the nest and on their teeth so your chance of a serious infection or complications goes up. Now, it's possible that slowly pushing your hand gently in there wouldn't rile them up, but you don't want to find out you have a serious allergy by testing that theory right there.
SO think I'd be a naw on this nest, even though I'm not normall worried by siders at all. I almost always catch and release unless it's a Hobo and there's a chance it'll scurry into hiding. Because I'd rather ice it then than deal with my wife or kid finding it later. You'd think they were tigers rather than spiders, the way they react.
I once climbed through a spiderweb on the way up a ladder after jumping from a fishing village jetty and when I got to the top about a thousand baby spiders were cascading down my face and torso. I jumped back in the water so fast and panicked that I'm lucky I didn't decapitate myself on a mooring line.
I was itchy for the next twenty years.
EDIT. $100k! Hell yeah. I'd do it immediately.