How can I pass variables from awk to a shell command?

you are close. you have to concatenate the command line with awk variables:

awk '{system("wc "$1)}' myfile

You cannot grab the output of an awk system() call, you can only get the exit status. Use the getline/pipe or getline/variable/pipe constructs

awk '{
    cmd = "your_command " $1
    while (cmd | getline line) {
        do_something_with(line) 
    }
    close(cmd)
}' file