Paste this within onclick of that button (correct the url in 3rd line):
var script = document.createElement("script");
script.setAttribute("type", "text/javascript");
script.setAttribute("src", "url to the script file here");
document.getElementsByTagName("head")[0].appendChild(script);
That script will start being downloaded immediately after line 4 is executed, and as soon as it’s downloaded it’ll execute or otherwise be usable.