You can set one of the trackpads to ‘as mouse’, which lets you use the touchscreen without actually touching the screen. You could also do it with one of the analogue sticks as well, but the trackpads are more precise.
If you’re open to using the touchscreen, though, you could just buy a cheap capacitive touch stylus and use it exactly as you would on a real DS.
Dolphin is just a mess on the Deck. I was having an issue where it would get stuck in the ‘exiting game’ state every single time I closed it, so I updated Dolphin and it corrupted all of my saves. And it didn’t even fix the problem.