You have 3 problems, and all caused by yourself.
The first one, you did not ask the requirements beforehand.
The second, you used PhotoIShouldNotUSeItForEverythingShop.
No. Depending on the assets included, and the type of design, there is a biiiiiig chance you need to make it correctly. In a vector-based program.
If you really used paths in Photoshop, (Which means you used almost entirely the pen tool) you can export the paths to illustrator, and simply open these paths in Corel.
The third one. If someone asks a file in an editable program, it could mean that they do not trust your work to be properly prepared.
In this case, it is obvious that you do not know how to prepare a file to be printed as it needs to be.
Does it have the correct bleeding, color separation, spot colors, vector-based texts, overprint settings, a separate layer for the cut, and a big etcetera?
I must say. I work in Corel Draw and I Never, ever send a Corel Draw file.
I always send a PDF file with "no mistakes" on it, to be printed in the plates directly.