Photos won't open because Mac thinks they're an app downloaded from an unidentified developer

USB SD card reader is like this:

Mine doesn't look like this, and I'm not recommending this one, but it's a nice picture. Also, it has USB-A and USB-c connectors, and it only costs $10.

I plug in my 2 SD Cards from my Nikon to get pictures, NEF and jpeg, into my Mac. It's the most reliable method, I think.

As to why AirDrop doesn't work-- we don't have enough information to know. Are you doing a few images at a time? That's best for AirDrop.

Have you tried these things?

• • Restart the computer (of course)
  • Re-start in Safe Mode. This bypasses certain potentially disruptive processes. Safe Mode is different for different computers, so see this: 

           Start up your Mac in safe mode - Apple Support 

• • Make a new user and see if the same problem recurs with it

Let us know your results....

Instead of opening the new files with Photos try to import them to Photos. Can Photos import the Nikon RAW files or do you get an error message? If yes, what is the message?

Can you open the RAW files in Preview, when you select one of them from the File menu or use ⌘O in Preview?

You can get files from your D40 using a USB card read if all else fails and that's a lot more simple than that airdrop manoeuvre you're doing.

It sounds like OS is recognising these images as applications, and I wonder of the .nef suffix has been lost or damaged in some way. Try remove that suffix and tap it in again and see if that changes things.

The default app for images is Preview.app so try to set it as default (it can be GraphicConverter, Photoshop etc but try setting the default first because that settings seems to be incorrect now).

Go to settings > privacy > and tap on “open anyway”. This allows you to open “dodgy” apps.

I hope this fixes your issue :)