Is it possible to build a fake flash drive for the TV that is in reality a share drive?
Although product recommendations are technically not meant for this forum, this is what you want: https://www.amazon.com/SanDisk-Connect-Wireless-Stick-Flash/dp/B00ZCFYT5K

You could try looking around for cheaper alternatives, like this:
https://www.amazon.com/Wireless-Airdisk-WiFi-External-Storage-Android/dp/B082M5CGLS/