Yes, you would also need to make sure that you use the correct rom. For WWF No Mercy, there were two separate North American versions released: version 1.0 and version 1.1. Even though version 1.1 is newer and fixes a save glitch, I mainly work on projects involving version 1.0 because it is the version that most cheat codes you find online are made for. So, if you are wanting to use cheat codes on the EverDrive, make sure that you are using version 1.0 (as well as the game's master code). If you are wanting to import a save from Project 64 after save swapping it, make sure that the save file for the game version you played on Project 64 matches the game version that you are going to play on the EverDrive 64.
In addition, if you have not done it yet, try making sure that you have selected the save file to load on the EverDrive before you start the game the first time.