Hooking audio compressor to mains without chasis
Have exposed mains is dangerous, and I expect you know that. This answer only talks about how to do it, not if you should do it!

That being said...

You do want to bring all of your grounds together. This can be to any piece of random metal that you can firmly connect them to.  If you had ring terminals, I could envision each ground wire being terminated with a ring terminal, and all the ring terminals connected around a bolt with a washer and nut.

Don't forget to hook up this big node of wires up to the ground wire in your mains!  It doesn't do any good if it's floating.  And, of course, make sure it can't make accidental contact with the live circuitry.

Also, for a project like this, I always try to plug it into a GFCI outlet.  If you don't have one available, you can find an extension cord with an integrated GFCI.  This way, it ensures that your ground node won't get "hot", in case anything goes wrong...

Good luck :)