Unless you are storing long term, like 8-12 months in a bucket, oxidation really isn't an issue. The plastic is ever so slightly permiable, but the fermentation keeps a blanket of CO2 above the beer and always below any oxygen, because CO2 is heavier than air. As long as you keep the top closed and don't open it over and over, there is a negligable chance of oxidation.
Adding the wine perserver would present a higher risk of oxidation than just leaving it be!
Just always do a 2-3 week primary for average to low gravity beers (anything under 1.07 or so), and 99% of the time fermentation will be complete without you having yto open the bucket at all to take a reading, THEN take your FG reading, instead of trying to rush it and time it to pull out of the primary exactly when it hits FG. The extra time in the bucket will not only get you to FG, the yeast will also clean up off flavors AND the beer will start bulk conditioning.
Don't overthink it or try to rush it. Patience is a key ingredient in good beer.
Primary #1 - Midnight Ryeder (Midnight Wheat and Rye)
Primary #2 - Florida Weiss
Primary #3 - Kane-DOH APA (Honey Citra APA)
Secondary #1 - Downtown Flanders Brown (brewed August 2012)
Keg #1 - Raspberry Florida Weiss
Keg #2 - Cinnamon Raisin Cider
Keg #3 - NONE!
Bottled - NONE!