I would leave it as is and open and close it with care. IMO the value as a collectible would be compromised no matter how beautiful the scales might be that replaced the originals. Many collectors of Case Bros razors do not shave with straight razors and the utility of the razor wouldn't be an issue for them but the replaced scales would.
OTOH, thinking of my Puma with Kayser Ellison steel blade on which you fitted the beautiful micarta scales. I would never sell it and leaving it with the original scales made it useless as a shaver so being able to use it was more important to me then leaving it as it was.
Then again my Puma isn't the collector's item that the Case Bros is. The Springville, NY factory was only operational for a short time and it is more desirable to collectors then the Case Bros Little Valley razors. I would think long and hard before I took those off of it. :shrug: I honed, stropped, and shaved with that and though the scales are not as tight as we might like the razor is usable as is.