There used to be this Asian dude on here from Essex (it wasn’t me) what used to go around the centre of London acting as a sort of “guide” like you get on explorations in faraway foreign lands telling random visitors from all across the world stuff like that Alligators were regularly found in the River Thames and Grand Union Canal (and to therefore be most careful when walking near these waterways) and that the cultural centre of London was in fact across the river in Peckham. Americans in particular would believe him without questioning a word.
The only problem i can see with doing it in Hyde Park isn’t that its controversial or frowned upon (quite the opposite) but you will be competiing with a great deal of people doing the same due to speakers corners etc, when I was at uni all the yoghurt weavers/lefties would meet up there for protest marches. This makes it hard to think up something unique.
I would personally have gone for a more random area of London – however you do have the advantage that there the special feds they have are far more likely to accept its a teenagers prank and in line with a tradition of public speaking in this area (and be more concerned over the heavier political speakers), whereas in a suburban local area rentaguards/borough metpol units are going to think its something to do with the urban music scene / “mc’ing” and that you are trying to start beef with rival gangs and at the very least move you on/discourage you (plus there might be genuine safety risk to yourself). Which is a shame as there is more comedy value in picking a less popular/obvious target.