If you want to use your own custom HTML element/button to launch the chat widget on a page, you just need to add the special classname "dpwidget-open" to it. For example:

<button class="dpwidget-open">Open Chat</button>

You can use some custom CSS on your page to hide the default button:

<style type="text/css">
#dp_widget_container iframe[name="widget_trigger_iframe"] {
    display: none !important;
}
</style>