The Y or not to Y issue at either the control amp or subwoofer end is to determine if the L and R line outputs on your control amp are actively isolated from each other. If not, then combining them through a Y connector will at best blend the two channels and give you wide band mono performance. At worst, you might damage your line circuits.
Assuming your subwoofer has stereo inputs and that its own inputs are actively isolated, then the safe mode would simply be a stereo cable connection from your integrated amp to the stereo line inputs on the subwoofer.
Regards,
Frank Van Alstine