The Wifi outlet seems like mega overkill to run a schedule. Couldn't you just use one of these? https://www.google.co.uk/search?q=socket+timer+us&safe=off&b...
Those normally work in 30min increments minimum, this stays on for 20 seconds, once a week. I already own a "smart outlet" so the cost for me would be less than $10 to build this, I just got into growing herbs and this would be a really awesome setup.
This wouldn't work if you want 1 minute a week (since the cycle repeats every 35 minutes), but for hydroponics sometimes you want a short duration with very frequent repetitions, and the electronic timers (which are preferable in most other ways) don't provide enough on/off cycles per day or week.