So, if you're offering all cash, the seller won't expect there to be an appraisal contingency anyways, so those two deal points are kind of the same. An appraisal contingency is generally nested inside the financing contingency, which you won't have if you're offering all cash.
Not sure what market you're in but it's usually wise to be only as aggressive as you need to be to get the property tied up. If you waive the inspection now, maybe you can still back out later, but then it's all been a waste of your time. Assuming you find problems, what you really want is leverage to renegotiate the price, and that leverage generally comes from having a clear right to walk away at absolutely no cost to you.
Finally, if you don't do an "official" inspection report, it's nearly impossible to get a seller to take your discount request seriously. You want to be able to back up your $ request with a written expert opinion. Seeing the physical issues spelled out on paper, often with photos, generally gives sellers more reason to accept a pricing discount or seller credit request.
Hope that helps! Good luck.