Any risk for putting a grounding adapter for a non grounded electrical appliance

Factual Questions
1

I got some with some disability issues a set of remote control outlets like this.

The wall outlets have no grounding outlet. The electrical appliance (fans and air purifiers) do not have grounding prongs either. but the remote outlets do.

would using a grounding adapter like this pose any kind of risk if it isn’t screwed into the grounding screw?

I don’t really understand electricity, but if the appliance you’re plugging in (like a fan) has no grounding screw, does the adapter need to be connected to the grounding screw?

2 prong outlet ← 3 prong grounding adapter ← 3 prong grounded remote outlet ← 2 prong electrical appliance.

In that situation do you need to ground the adapter?

2

Yes, you should ground the adapter.

The appliance may not have a ground pin, but the remote adapter is also a device/appliance and is expecting to be plugged into an outlet with proper grounding.

3

There is also the risk that someone, seeing a three pin outlet on the adapter, would assume that it is grounded.

4

If the receptacle is two pin because there is no ground wire in the wires, hooking to the cover plate screw does nothing.

5

Generally small electronic devices that are in sealed plastic cases do not require a ground. My remote control Insteon adapters have grounding pins only to pass it through to the device plugged in.

I would go ahead and use these, but fill the grounding hole with superglue or something so no one attempts to plug something that requires a ground into it.