It's probably best that I wait until I see a picture. Regardless, you could buy screw-down pushers from Ofrei ("Daytona white screw down push button"), CousinsUK, or Clark Watch Parts. I don't have any first-hand experience with any of these, but both Ofrei and Cousins units have been highly recommended here. I don't know anyone who has tried Clark's, but they look good in the pictures.
Whichever Daytona you have, the best-case scenario is that the pushers will thread in with no problem. At worst, you'll need to drill out the pusher threads and glue the new pushers in place. This is very likely on a DW case, which has threads that are the correct diameter but have the wrong pitch.