The AIR pump is pretty easy to check- just find the wire going to it and trace it back to the connector (probably next to the coolant reservoir) and unplug the wire. If the sound goes away, voila. It has a magnetic clutch just like an AC compressor, so, no wire = no engagement of the pump.

You can leave this wire unhooked, no problem at all, as stated above.
However, I think it might be a good idea to also disable the check valve on the outlet side of the pump. This valve opens via a vacuum line when the pump runs, allowing the air to enter the exhaust manifold. If the pump were disabled and the check valve opened during initial wartmup, would the hot exhaust then be able to travel back into the pump and fry it?
Just unhook and plug the vacuum hose to be sure.

DG