You should be fine to submit runs without the top of the screen. There are a lot of ways to find out if someone is cheating and that alone is not a big concern.
I should also probably mention though that you don’t have to submit your runs. At the end of the day we speedrun for fun. I have a 5 flat and I haven’t submitted a single run to the smb1 leaderboards.
I know there are some ways to play on mobile but I don’t know how or if it is allowed for speed running. You may already know this but I want to make sure. If you have a Wii a WiiU a Switch, and maybe some others you can easily play on those and it is excepted by the community although it does run at a slower frame rate, so you will have slower runs than someone running on the right emulator or the original hardware.