First:

Don't do that. The protector BMS needs to be always physically with the cells, not elsewhere. Connect the BMS permanently to the cells. Do not rely on a BMS that at times is connected to the cells and other time it is not. When the BMS is not connected to the cells is when you'll blow up your battery.

Second:

Instead of needing to press a switch, simply place an "ideal rectifier" circuit between the charging port and the protector BMS (permanently connected to the cells). For example, see this instructional page

First:

Don't do that. The protector BMS needs to be always physically with the cells, not elsewhere. Connect the BMS permanently to the cells. Do not rely on a BMS that at times is connected to the cells and other time it is not. When the BMS is not connected to the cells is when you'll blow up your battery.

Second:

Instead of needing to press a switch, simply place an "ideal rectifier" circuit between the charging port and the protector BMS (permanently connected to the cells). That circuit will let power flow into the battery and prevent power from flowing out of the battery into the charging port. For an example of an ideal rectifier, see this Stack Exchange question.