We need a solution that will allow us to temporarily share secure information with our remote sites

So let me elaborate a little (thank you for the responses at this point).  Maybe my further details will change your responses, or maybe it won't.

I have UserA that needs to give UserB sensitive information (possibly just name/address, intercompany data, etc.).  Not necessarily credit cards, but information that should be viewed once and then gone from history.
We want them to transmit the data using something other than a phone call and we want that data to be destroyed after the recipient reads it.  Almost like a Snapchat deletion feature.  
Does that change either of your answers/suggestions?  

Thank you again for your time.

Do you have control over UserB's computer?

If not, then there's no way you can totally control what they do with the data you send them.

Theoretically, we would be able to have control over user B's computer, but it would not be feasable to lock down a specific computer just for the sake of making sure User B does not make copies of a specific file, or copy.

Are there any software solutions out there that may achieve what we are looking for? Perhaps, something like dropbox, or a chat program that can perform this task?

You could set up a group policy to disable flash drives on that PC, and that would be helpful. You could also look at blocking email on it.

As for any kind of file service, I know there are some things out there but I have not personally used them and can't recommend something specific.  At the very least, you could look at file encryption which would at least make the file harder to open if it fell into the wrong hands. Basic password protection on files can be a deterrent.

The problem is access to data. Once they access that data, it's out in the open. A cell phone with a camera will bypass anything you might put in place if they can get data on their screen. You can establish internal policies and tell employees not to copy data, but trying to guarantee it with software is just about impossible. I mean, some people can even memorize a credit card number. It's only a few digits longer than a phone number.

Think of it this way - you can't show somebody something then force them to forget it. What has been seen cannot be unseen.

Thank you both for the information. It seems that there is no real way to accomplish what I'm looking for.
I do appreciate the input and your time.