You may not need to remove the exhaust manifold.
If you undo the jubilee clips that hold the rubber elbows on to each end of the manifold, once removed you then have access to each end of the tube nest. The tube nest can be withdrawn, from the forward end if memory serves me correctly, but before you remove the tube nest, note very carefully which end of it is the forward end and which is the aft or stern end so that when you put it back after cleaning, that you get it right first time. Sometimes the tube nest can be a little reluctant to move, but be very gentle with it if you have to use a rubber or wooden mallet, (do not use a hammer unless you are entirely happy with the thought of paying out for a new one and waiting for it to arrive). Once the tube nest is out you can wash it through with water both through the tubes from one end to the other and probably more importantly around the outside and between each tube. Elsewhere within the postings on the forum some have suggested use of some fairly powerful chemicals, but I would not recommend such chemicals, better to be very gentle. Quite how the tubes are fitted into the faceplate at each end I wouldn’t swear to, but in larger installations such on ships engines, the ends of the tubes are expanded hydraulically, and it would not surprise me if the same method is used, so do be careful not to dislodge any of the tubes.
With the tube nest out you can clean the inside of the now empty manifold.
Take lots of photos before each stage of dismantling so that you know exactly how things go back together, and don’t forget to check the insides of the rubber elbows and renew them if there are any areas of obvious wear.
Don’t be surprised to find pieces of impeller vanes or barnacle shells within tube nest or in way of the elbow at the water inlet end, especially if you are not the first owner of the boat.
Good luck, hope it goes well.