If I remember correctly, much of that design uses rivets for strength and soft solder should be fine. The bottom...where the heat is...has liquid in it. This is what keeps it from heating to the point it would melt. So long as you don't boil it dry or run it dry...that solder shouldn't be a problem. It takes about 1200-1300 F to braze. That's when the copper is "cherry red". So, brazing..inherently means you are annealing the copper (it will be soft after you braze it, dent easily, etc) . And as was said above...copper soaks up the heat. It takes a LOT of direct heat to get it up to brazing temp.
Some people do/use a bit of both. ie., they braze certain joins/parts to make them extra sturdy. Like the bottom, the lynearm where it connects to the head, etc. If you decide to do that...make sure you do your brazing first. Because heating the copper to brazing temps will only melt the soft solder anywhere near it. You can soft solder all day long right next to a brazed join and it wont' budge.
Another old trick is to use a wet rag (or something to cool with) when you have an already soldered join or seam you are trying to protect. It works...up to a point.