You can definitely do this with Harmony. If it wasn't expensive (which really all you need is the hub and those are often found for less than $100) then I would simply use that if you have no other use for it. Harmony can learn any IR remote commands.
I use Dan's driver with my Harmony hub. It's local, so it's fast and will work when internet is interrupted. For triggering, just create an Alexa routine to turn on one of the virtual switches that the integration creates.
There are other IR options too.
