Best ways to get pictures onto a program.

Can you transfer your phone photos over a USB cable?

If you use Fixture Builder you can do screen shots from it. Or a cad program

Take a picture with a phone and transfer the photo by cable into the computer (android and windows if microsoft still makes a phone OS)
Get a better camera and do the same thing. (this can be a cell phone with the SIM pulled so it can't call anyone, and you can disable Wifi on it as well so it is standalone other than cable)
Tablet and transfer by cable.

Might be a no go on the phone/tablet altogether though, depending on what your boss is referring to, though in the extreme, you would likely also have problems with the SDCard. Anything our congress can do to make us less profitable and unable to compete globally, they are there for you!

If he just doesn't trust email, is it because you are using a personal email on your phone (I'm presuming a phone since you are emailing pictures)?
If you put your company email on your phone with a 3rd party email client, do his concerns go away?
Personally, I'd be more concerned with your business email on your phone, but I don't know what he's exactly concerned with.

Webcam with a USB cord extension so there is no wireless communication?

If that's all a problem, you're going to have to go with the fixture builder thing, or have someone draw tooling into a CAD package with a model in it and do screen shots as Kingsld1 said.

It's not so much the email thing, I think it's more taking pictures and having them backed up in the cloud auto-magically.

I think a disconnected phone transferring via cable is the best way, I'll see about going that route.

We have an older camera with an SD card. I take pics then remove the SD card and stick it in the SD slot of the hexagon supplied computer and push the external object command button and pull them right off the sd card.

tell them to get you a company phone for taking & transmitting pics, or get a better camera that can automatically upload via wifi (plenty of quality cameras have this feature nowadays). explain the cost savings in the amount of time it takes you to generally do it otherwise.

tell them to get you a company phone for taking & transmitting pics, or get a better camera that can automatically upload via wifi (plenty of quality cameras have this feature nowadays). explain the cost savings in the amount of time it takes you to generally do it otherwise.

I work at one of the most ITAR controlled companies in the world and we have dedicated cameras (Olympus Tough TG6) for uploading photos directly to the PC / network.

I work in an ITAR company also. If you use a personal phone please make sure it does not go against company or government (if applicable) policies.