I would be cautious about applying anything to his foot. He is naturally going to pick at it and will ingest whatever it is. While turmeric is safe for parrots, in small amounts, he could easily ingest a toxic level. I’m not sure about mustard oil. As far as being an oil, any oil or salve will affect his ability to control his body temperature, because if too much gets on his feathers, it will cause them to mat and lose their protecting oil coating. There are some herbs that have anti-inflammatory properties, but you would have to research to try to find out how much to give him. It can be very easy to give a bird toxic levels of anything if you give even a little bit over the recommended amount.
Thanks for the update,