Sure...
but if it pleases the court...
I am the family archive and have been scanning old pictures and negatives for several years now.
Doesn't tell me that you have been distributing copies to family members just that you are given photos and are archiving them. Assumption was that you were just maintaining a backup for those photos should they disappear, get destroyed, lost, etc. Also, if you have been doing this for years, every single image was taken by somebody and they own that copyright, correct? It has nothing to do with whether a professional photographer took the image, if there was an ethical issue here, you already breached it potentially, correct? 
Recently I was handed a large stack of professionally taken portraits and kids sports shots. These are rather old, somewhere around 30~60 years old, some more. They are of kids (mostly family members but some team pictures as well), taken by some portrait studio or other professional photographer, but they are not watermarked nor identified in any other way.
This has to be looked at from a public domain perspective, which requires a lawyer. I know that public domain applies to graphics and artwork. There are countless images online through clip art and image gallery sites that are now considered public domain. The question here though is whether old images with no copyright info also fall into this, the age, etc. There are a number of issues around this, so I have to soften my stance on this a bit, and again why I suggest just doing a free consultation with a lawyer.
https://www.legalgenealogist.com …and-the-old-family-photo/
This paints a dismal image of what you are trying to do, but I think the gray area of the law comes to your rescue, this article is full of what-ifs and a very strict interpretation of law.
So, is it ethical to scan the photos? Your thoughts? To me it seems rather gray. I am not producing a derivative work but would copy exactly as is and restore if necessary. I would distribute the electronic images to several family members. I'm reasonable sure that the photos were not produced under a creative commons license agreement or work-made-for-hire agreement though I can't be sure as I have no idea who produced the originals. What would you do?
This lends credence to my assumption in the first part, that you were indeed not distributing archival copies to everyone, because you say that you "would distribute", meaning you haven't been, but will in the future. I was probably erroneous in this assumption. 