You shouldn't need an SSL certificate at all unless it's how your server is configured for security purposes. If that's the case native HTML5 for you would likely also present the same problem.
May I ask a quick one on the controls css?Just while I'm here and relevant material is already present on the post. Re: I get a blue background around the controls of the video, when it should ideally be transparent
Pretty sure they're just button elements and the button styling from your template is changing them. Notice the buttons in top right have same styling.