This will work fine but may get over written when you go to upgrade your umbraco instance. Instead how about write an extension to append the class onto the embed.

Highly recommed paul seal you tube series on building a website with umbraco 8. He writes a HtmlExtensions for images that appends the img-fluid class onto images in the grid - https://youtu.be/PmAYWmH9BhE which you could easily adapt.

 public static class HtmlExtensions
    {
        public static IHtmlString GetGridHtml(this HtmlHelper html, IPublishedContent contentItem, string framework, string propertyAlias, bool fluidImages)
        {
            if (fluidImages )
            {  
                return html.Raw(html.GetGridHtml(contentItem, framework, propertyAlias).ToString().Replace("<img ", "<img class='img-fluid' ");
            }


            else
            {
                return html.GetGridHtml(contentItem, propertyAlias, framework);
            }
        }
    }

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