In the Style Picker > Action > Copy Link to Clipboard
edit the html in Notepad++ (free)
use Search > Replace
Find what: (<tr>\s*\R\s*<td>)(.+)</td>

Replace with: $1<a href="$2.m4a" title="" target="_blank">$2</a></td>

Check > Regular expression

then save, this will give you an html page that will open in your browser as here
when the style name is clicked it will open the m4a demo file in a new tab to play.

If you want to use local demo files
Reaper has a batch converter that will convert the wma to mpeg4 to play direct in the browser.
File > Batch File/ Item Converter
just change to the local path where the demo files are.

Here's the html file that you can open locally on PC or phone with web browser:

Attached Files (Click to download or enlarge) (Only available when you are logged in)
BB23-HTML-Styles.png (120.67 KB, 16 downloads)