If you're going to naturally carbonate in the keg, the beer will have the appropriate carbonation level, so all you need is enough CO2 to push the beer out to a faucet. That doesn't take much CO2 at all.
If you're going to use a picnic faucet, just make sure to use a long enough beer line to it to avoid gas breakout/foamy pours. You'd need at least 6 feet of 3/16" vinyl for a typical 2.4 volume carbonation level.
With respect to the carbonation in the keg, when you fill the keg and add the carbonation fermentables, ideally you want to purge the oxygen out of the head space, and then apply enough CO2 pressure to the keg to get the lid to seal. I'm not familiar with "soda chargers", so you'll have to investigate how you can handle at least the latter if not both issues. If the keg lid doesn't seal tight your natural carbonation process will fail...
Cheers!