They are rear air shocks...

The gas struts are for the front, no...?

The original ones are, I thought you were going to get gas shocks because you were not sure the pump worked anymore.
Which left the manual fill with air way, or gas conversion.

Yeah, I guess my posts are somewhat confusion... sorry about that.

As you, and others, can probably tell, I don't know all that much about cars - that is why sites like this are so helpful.

I do not know if the air compressor works or not - I think I hear it sometimes...

So, I ordered the KYB SR1002 Excel-G Air Shocks that are supposedly a recommended OEM replacement - you can see them here on Amazon
So, if the air compressor doesn't work - I just have the guy installing them put 40lbs (?) of air in them - and all is good...?

All good, no worries.
If the compressor works it only comes on when the weight changes in the trunk a good bit, it keeps the ride level.
If it does work a tip to keep it going longer is like once a year take some light sewing machine oil, remove the hose coming from the pump and squirt a lil oil up in there.
This is what I used on my 96 Park Ave'* pump..

If those do not work with the pump you will need this kit to be able to fill and let air out of it to keep the ride level.

I very rarely have rear seat passengers...

And nothing ever all that heavy gets put in the trunk...

So if I have the guy installing the rear shocks just put in (40 lbs...?) - the shocks would just stay at 40 lbs, correct?

As long as he'* able to put the air in without the kit, which if the air pump can do it I am not sure why he couldn't.
Just have him check to see if the ride height is leveled.

If he does not know your factory ride height specs maybe this will help..

Would this be it...?

Ride Height : 2000-2005 (other than GXP)

That looks right, not sure on the actual specs, so I cannot say 100% they are right, but I would bet they are..
If the front does not set at the specs listed there just use the method where you don't know actual specs, and get the car level, getting it level is the main thing you want to do,

Make sure you have a way to check the air pressure as a general maintenance item. The reason there is a minimum PSI on air shocks is because the air bladders on air shocks/struts will destroy itself if it is run low.

So he may actually want to get that kit so he can easily check and maintain that set air pressure himself easily?

Probably a good idea.