I'm guessing there's no switch lite capture card? You could always get a camera and point it at your hands (and thus the game console) while you play. The mods probably won't reject your run for that.
I would say, if you can, get a regular switch to make it easier. if not, try to connect your switch lite to a TV if possible.
The easiest way would be to just point a camera at the screen. It's perfectly allowed and even a former wr used that method of recording.
if you have access to a laptop, use the laptop camera and angle it to the switch, it still gives good viewing angles for yourself and the camera to capture the game, just make sure its done on a flat surface, like a coffee table so the laptop doesnt overheat
Following Twitch’s announcement regarding the 100-hour storage limit for Highlights, the SMB1 mod team recommends that runners reupload any previously submitted Twitch highlights to a permanent video hosting website (e.g., YouTube) and resubmit any submissions labelled as "at-risk".