For surgery on the vocal cords the surgeon wants a beam that cuts cleanly and barely burns the tissue around the cut, because the larynx is tiny and the voice depends on intact mucosa.
The carbon dioxide laser wins on this. Its long $10{,}600$ nm wavelength is soaked up almost entirely by tissue water, so the energy stops at the surface. The result is a precise incision with very little spread of heat sideways. Mounted on the operating microscope with a micromanipulator, it lets the surgeon vaporise papillomas, treat early cord cancers and divide webs with great control. That is why it became the routine workhorse for laryngeal procedures.
The competitors serve other niches. The Nd:YAG beam goes deep into tissue, which suits debulking large tumours lower in the airway but is too aggressive for cords. Argon is mostly an eye and vascular laser. KTP handles vascular lesions and finds some use in phonosurgery, yet it has not displaced CO2 as the default.
So for everyday laryngeal surgery the answer is the deeply water absorbed, shallow cutting beam.
\[\boxed{\text{CO2 laser}}\]