I looked at Sigil, but Kindle doesn't read epub so it wasn't much use. The resultant file would still have to be converted. For Kindle you have to have mobi format which is also a specialised HTML file. I format the songs as html, then use Calibre to convert them to mobi. Works fine, though Calibre is prone to cause my Linux Mint OS to crash which is a nuisance.

As you only need a limited number of html tags I simply save the words of the song as a plain text file then add the html tags using a plain text editor. I have "template" file with the basic html header and body tags together with the tags I mainly need which I can copy and paste into the song file. The text editor I use highlights the tags with colour when the file is saved with a .html suffix. I find this almost as quick as using a dedicated html editor and you retain total control over your html, unlike many html editors, especially the WYSIWYG ones which add a lot of unnecessary bloat.