Happy to hear if there are glaring problems with this approach, but if you can assume files named with version numbers, you can use a script to always launch the newest…

#!/bin/bash
cd ~/Downloads
chmod +x $(ls | grep Appname.*AppImage$ | sort -rV | head -n 1)
./$(ls | grep Appname.*AppImage$ | sort -rV | head -n 1)

Or you could change the script to sort by file modified date and launch the newest.

edit: Discovered an issue with version numbering like .10 and learned about the sort -V switch that fixes it!