How to hide AppleTVs from the phone speaker options?
Turn off air play on the apple tv.

Otherwise the only way is to place the apple tv or iphone on different networks.  This can be done by creating a vlan and a new essid that tags network traffic to that vlan. Plus routing rules to give the vlan network access to things it needs (internet).

Or possibly create a new subnet and setup routing so the 2 subnets cannot communicate but still allows Internet access.