To really stop oxidation without additives the only option is remove or displace oxygen. Inert gas purge is your best option.
Nitrogen purge would be my first move but to completely remove oxygen from the environment before packing you are going to need something like a glovebox.
Basically put your filled containers in here uncapped, and get an oxygen sensor. Purge the box with nitrogen until your oxygen sensor reads ~0 and then cap.
Alternatively you could use argon as it is heavier than oxygen and will displace the oxygen in the container, creating a blanket. This is used widely in the wine industry.
With argon you could gently blow it into the container and then cap without worry of it escaping or remixing with air before you close it.
As will all things including gas (especially argon) do this in a large open space with good ventilation, these inert gases are not toxic or flammable but both can lead to asphyxiation if a tank is left on or decides to leak. Bonus points if you have an oxygen monitor where you store your tanks.
Edit: This is even a cheaper option to completely remove O2