Adding a shortcode inside of a Javascript InnerHTML

Hi, I was wondering if it's possible to insert shortcode inside javascript to output different forms selected from a dropdown list.

I can make the attached script work if I paste it the form's actual html (into a Visual Composer Raw HTML box), but I was hoping to just stick the shortcode in there. Right now it's just outputting the shortcode itself.

Here is the script I am using. Is there a better way to do this?

<!-- JS -->

<script>
function show(form)
{
	if (form=="")
	{
		return;
	}

	else if (form=="start")
	{
		document.getElementById('FormArea').innerHTML="[si-contact-form form='8']";
	}
	else if (form=="part")
	{
		document.getElementById('FormArea').innerHTML="[si-contact-form form='9']";
	}

}
</script>

<!-- HTML -->

<select name="ContactSelect" onchange="show(this.value)">
	<option value="">- Select form -</option>
	<option value="start">I want to START a Venture Village</option>
	<option value="part">I want to PARTICIPATE a Venture Village</option>

</select>

<div id="FormArea">

<!-- ( form ) -->

</div>