Deleting the app will delete all your data, so you would need to export your databases and write down your settings first. However, the App Store might not let you reinstall the app afterwards, so you would risk making the device completely unusable for Set List Maker.
This seems to be an ongoing problem with the App Store where you're supposed to be able to install the last supported app version for an old iOS version, but that's not actually available. I went back and forth with Apple on this for several months, but they never acknowledged the problem or offered a solution. You could try taking your iPad to an Apple Store and see if they can make it work. Otherwise I think you will have to live with the alerts until you upgrade to newer hardware.
If you do go to the Apple Store you can tell them:
your installed app version: 2022-08-12
last supported app version for your iOS version: 2022-09-16
current app version: 2023-05-05
Version 2022-09-16 is marked on my end is being available to install on older devices, and this works as advertised for some people but not others. I don't know if the difference has to do with your device, your App Store account, your location (country) or something else.