I've done this conversion, and...
would suggest that if you're going to have a .257 Roberts, you use a decent 98 or Springfield to start with!
The Adams & Bennet barrels that Midway advertises for this action is out of stock, has been for a long time, and has a long wait...AND...they're only 21" long. The Roberts can use 24" effectively, and they have the longer barrels available for the large ring actions.
I had one of these actions barreled as a first rifle for my oldest son. It didn't take long to tire of using the low-performance, non-+P ammunition in the thing, and wanted to boost the load up to where it should've been all along.
Not wanting to spark a controversy, you could probably use that '93 for the rest of your life and not have a problem with it. Mostly for ease of obtaining parts, accessories, and finding someone willing to work on it, I suggest the 'better' actions. If you've got scads of time, and willing/capable of doing the work yourself, then by all means have a ball......
Use the original ctg for the 1893 Mauser
I would not re-barrel the 93 Mauser to .257 Roberts or .250-3000 Savage. I would re-barrel it in 7x57mm. There is nothing wrong with the 7mm Mauser.