The games are encrypted with a console specific key so you can't copy any game off the SD card or emummc without the 'old' Switch. If the new Switch tries to use the game, it can't read the game because it has the wrong key.
If you used an emummc and have the prodinfo keys of the old Switch, then you can extract the save games.
There are some topics already here on how to do that.
Without prodinfo keys, you can't read the emummc files.
Sometimes that key file on the SD card in the root or /switch folder and they are called keys.dat.
If the new Switch has the same firmware version as the old Switch, then you should be able to use Hekate/Atmosphere as-is.
Hekate/Atmosphere are not encrypted in any way but do care about the firmware version of the Switch.
But you can grab the latest files from the internet and copy over the config files.