Quistgaard desk hinges  

If the holes line up...
Why don't you just modify the new ones to fit. Shouldn't take too long to take an 1/8 inch off either side with a grinder or belt sander.

I did consider that
I also thought of taking Exacto knife and wood chisel to carefully remove enough wood to allow the hing to fit. I guess six of one a half a dozen of another.
Thanks for you thoughts,
Mike

I wouldn't modify the desk...
If you modify the desk to fit the hinge then to my mind you damage the value, greatly, at least if I were the buyer. There is no going back from that modification. Modifying a new hinge to fit is true to the ideal of restoration that you change as little as possible. As a purchaser I would respect that.
You could also get a cnc shop to fabricate new hinges.

I can't help you with your hinge problem
... but that Lovig desk with the flip top is not a Quistgaard design. This is another of the many misattributions that are propagated on the internet.
It's a beautiful design, I have one. But it's not by Jens Quistgaard. There is absolutely no evidence to support that attribution.
This staved teak table with reversible top is not by Quistgaard either, regardless of how many eBayers sell it as his design.

Pegboard
I was thinking the same thing when I saw this post. At some point some saw Lovig Dansk on one of these and made a bad assumption then every one else fed off of that.. The word Dansk simply means Danish as best as I can tell. I can see where it started with the American company naming itself essentially "Danish".
To the OP's question. Definitely do not cut the desk. Modify the hardware to fit or have some custom made. It will be more expensive initially than cutting the wood, but you will devalue the desk enough that modifying the hardware is in reality the cheaper way to go.

This desk as you guys have...
This desk as you guys have mentioned is not designed by Quistgaard. It was designed by Peter Løvig Nielsen.
Attached a photo of how the desk is commonly marked on the underside.

Thanks for all of the great input.
I really appreciate your advice.

replacement hinge source
part no. 341.32.502 at hafele.com appears to be the one we need--I searched and searched but it wasn't until I started searching for 65mm x 30mm that I got anywhere.
https://hachol02.hafeleonline.com/OA_HTML/ibeCCtpItmDspRte.jsp?sitex=100...