Insert favicon in sitemap

Hello, to display the favicon in Bing search results, I followed the guidelines. I placed the favicon.ico in the root of the site, inserted the meta tag in the head of all pages, and submitted the absolute link of the favicon.ico in Bing Webmaster Tools. Now, regarding including it in the sitemap, since I use WordPress and have the default sitemap that I can't modify, I thought of creating a dedicated XML sitemap for Bing containing only the absolute link of the favicon.ico and submitting it along with the main sitemap of the site in Bing Webmaster Tools. Would this work? Thank you.