For that, I guess we have to go for custom scripts.

We can achieve this in two ways. By updating the PegaHelper.js file to block the appending scripts to the page which renders cobrowse or By adding the scripts which hide and show cobrowse widget based on condition on the chat page.

The second one is simpler and worked for me as well. Here is the script which should be pasted on your chat HTML.

<style id="cobrowse">
        iframe[id*='firefly'] {
            display: none !important;
        }
</style>
<script>
  function show_cobrowse() {
  	$('#cobrowse').remove();
  }
</script>
<button onclick="show_cobrowse()"> Show Cobrowse </button>

The CSS hides the cobrowse "Support" button onload of the page. Hence, the Cobrowse widget won't be visible to the end-user initially. Onclick of the button, a js function is triggered which removes CSS block from the DOM which hides the cobrowse. Then the widget is visible for the user.

If you want to trigger the support button as well on click of the button, use the below script.

<script>
  function show_cobrowse() {
      $('#cobrowse').remove();
      setTimeout(function() {
	//find iframe
	let iframe = $('iframe[id*="firefly"]');
	//find button inside iframe
	let button = iframe.contents().find('div[id*="firefly"]');
	//trigger button click
	button.trigger("click");
}, 1000);

  }
</script>

Let me know if it worked for you.

Good Luck!