Print both without supports and choose which one to use for your project. Or split to objects and delete one from within the slicer.
I attempted to mix red, blue, and yellow PETG to create sort of a wood color. A center screw holds the wooden member in place. After I took the photo, I added additional, countersunk screw holes to the .stl file for secure mounting.
I am going to use this for a spool holder, so I didn't need the secure mounting. In fact, I wanted them to swivel. I plan to drill holes in the wood. Then get some wooden dowel and put pins in the ends to go in the holes, forming a roller to put PETG spools on. I will be able to twist them to take the dowel down and change rolls.
But you could add slots instead of holes to drop the dowel into or create a solid (non-moving) towel rack out of it. The whole point of using wood is to save print time and use what I had on hand. But you could easily print a roller or rack, and even print your own screws. But that is beyond the scope of this project.