I've actually been playing with laser diodes since before 404nm was available. I still remember the days of 30mW ps3 diodes being a huge deal and today 1.4W 440nm is something like 40$.
Gas lasers just have charm that diodes don't. After a while wiring diodes to batteries is just more of the same. I feel like a visible laser would be more fun to DIY. I might start with an ebay hene tube and go from there.
I've also considered gluing some glass tubing together and hiding a diode in one of the ends so that it looks like I built a gas laser
If the inner tube is slightly etched it might even look plausible from a distance.