Bobby Owsinski just wrote this blog..pertains to American airlines. I don't know how you'll do with United though.
good luck.
Michael
https://bobbyowsinskiblog.com/2019/06/06/american-airlines-music-gear/
also here's a link to united airlines policy for musical gear
http://www.airline-baggage-fees.com/flying-with-musical-instruments/united-airlines/