Rolex won't have a problem doing this. You can even have Rolex do it themselves if you want. They'll do it as long as dial you want is the same 'class' as the original dial and was offered on the watch originally, or is a diamond dial upgrade. I've looked into having my wife's DateJust dial replaced with a different one, and was told by Rolex this is fine, with the above caveats. As to cost, the DateJust cost was $150 for the dial (they will keep the old one if Rolex does it and they will require your AD to keep the old one to send back too) and a service cost. Since the movement is being uncased, they require it to be serviced. The only exception is if it's within 12 months of original purchase, then the servicing wasn't required.
I'm assuming the Daytona dial will be a little more than a DateJust, so I'd guess $300-500 for the dial-swap, plus a servicing fee.. Watchbreath's $800-1,200 estimate is probably about right.