You do not need to drain, but you can then expect coolant to leak until you connect the two. If you do drain the radiator, they will only drip/leak minimally.

You have to create a loop for the coolant so it goes back into the engine. You can drain the radiator first. Reuse the old coolant if it it still less than five years old. Buy a metal tube or elbow type pipe and hose clamps if needed. Connect the incoming and outgoing hoses with the tube or pipe and clamps.

There are special heater hose clamps that are a tool and you should use those to clamp the hoses before you remove the core. This will prevent the loss of coolant. Check an auto parts store.

Disconnect the hoses, close one end and try to suck all the coolant out of the heater core with a wet-vac or by pushing with compressed air.  That is all you need to do.  Make sure to top off the coolant and do a leak check after installing the bypass.

No don't drain them as you will just end up with excessive air in the system. In fact if you can clamp near the ends with mole grips it will save spilling coolant.