Short answer: no you can't.
Long answer: you might. If the user is running Internet Explorer and ActiveX is enabled, plus you know the installation path, you might by using:
<script type="text/javascript">
function runProgram()
{
var shell = new ActiveXObject("WScript.Shell");
var appITunes = "\"C:\\Program Files\\Path\\executable.exe\" ";
shell.Run(appITunes);
}
</script>
Another possibility would be to use Silverlight, which also works in Firefox if installed and given insane levels of access... (a.k.a. shouldn't happen)
<script>
dynamic cmd = AutomationFactory.CreateObject("WScript.Shell");
cmd.Run("calc.exe", 1, true);
</script>
Now the only true option you have, would be to register a custom protocol, which then triggers your program. This can be done as described here: https://support.shotgunsoftware.com/hc/en-us/articles/219031308-Launching-applications-using-custom-browser-protocols