Use @font-face to embed a font that contains emoji (I think that is quite rare, but this seems a contender: https://emojisymbols.com/).
Use @font-face to embed an icon font and wrap all emoji in spans that use that specific icon font.
Write javascript* that replaces all emoji with images just before you fire the print command, like this:
onclick="replaceAllEmojiWithImages(); window.print();"
*The javascript function can be derived from: https://stackoverflow.com/a/64007175/2397550