Who expects radios of any sort to work without antennas attached? A better question might be why Wi-Fi worked at all in that state.
Wi-Fi uses a lot more transmit power, so it's better able to make up for the extreme attenuation that comes from not having any antenna connected.
Not only does Bluetooth use a lot less power, but modern Bluetooth audio uses all ...
From the T440S Hardware Maintenance Manual.
The steps below give you the color codes for the wires
I think from your description that you should be OK
1040 Wireless LAN card (correction to this post)
Plug the gray cable into the connector labeled MAIN or 1 on the card
Plug the black cable into the connector labeled AUX or ...