Not just "cheap" but likely can be put together from stuff you have lying around.
If it doesn't work out for you or you prefer to spend the cash, there's nothing lost in starting out with the picnic tap and bottling wand approach.
Also, if you're really concerned about O2, you can purge the bottles from your tank prior to filling. Put a QD on the gas line and use an air-gun attachment from a compressor kit. You can stick a hose on this to get it to the bottom of the bottle. You could also T the gas line if you want to.
Since I have all this lying around anyway, it's essentially free for me. Plus, I don't bottle enough to warrant the investment in a beer gun anyway.