As the other person said, if your scripts are executables with an sh or bash 'shebang' at the top, they will continue to use the same shell they always did.
But if you did want to run them with zsh, most simple scripts that just set environment variables, string together commands, or redirect to files should work without any changes. The most obvious difference for basic scripts like that is that zsh doesn't split parameter-expansions on white space by default (so if you did something like `opts='-a -b -c'; mycmd $opts` it wouldn't work without additional, minor, modifications)
But if you did want to run them with zsh, most simple scripts that just set environment variables, string together commands, or redirect to files should work without any changes. The most obvious difference for basic scripts like that is that zsh doesn't split parameter-expansions on white space by default (so if you did something like `opts='-a -b -c'; mycmd $opts` it wouldn't work without additional, minor, modifications)