You should be able to just call the function directly using
$call_func
For everything else check out that answer: https://stackoverflow.com/a/17529221/3236102
It’s not directly what you need, but it shows a lot of different ways of how to call commands / functions.
Letting the user execute any arbitrary code is bad practice though, since it can be quite dangerous. What would be better is to do it like this:
if [ $userinput == "some_command" ];then
some_command
fi
This way, the user can only execute the commands that you want them to and can even output an error message if the input was incorrect.