Assuming this is a marine engine, and you say you've got a heat exchanger, I assume it's using canal/river/sea water for cooling? If so, you should have 4 hoses on your heat exchanger: Two will go to the engine, and the other two will be inlet & outlet to whatever water your boat is currently in.
It should be fairly straightforward to find which hose(s) go to the engine, but as for draining the system.... I think we'll need some pictures for that.
Here's a couple of pictures of one with a radiator on it (I think it's the same as yours, or similar at least):
(photo credit:
https://www.marinepowerservices.co.uk)
Looking at that, you've got a block on the front of the engine with both the inlet & outlet coolant passing through it. One way to drain the system would be to undo the lower fitting, but how accessible that is (and whether you can catch the coolant or not) is a question I can't answer... Actually, it might be worth giving Marine Power Services a call, see if they can steer you in the right direction?
PS: the "bottom hose" is visible on the 2nd pic, going to the lower LH corner of the radiator. Typically one undoes that hose, and watches the coolant fly everywhere except into the bucket you put underneath it!