I have been writing, drafting, and drawing out for probably more than a year now, about how to size, weld, and wire a 1:50 scale IJN Yamato Battleship, one I can actually ride in, drive, and (If it's legally possible) fire 9mm bullets from it's main guns. But I came across a problem. The scale calls for 0.32 inch thick armor at it's thickest, the waterline belt, and I wanted to make the whole thing out of aluminum because it's very light and very strong. But I can't do that, because it would not be bullet-proof. I would need a full inch of aluminum for the armor. So I thought, "Maybe I can make the armor out of steel, and the rest out of aluminum, or just make the whole thing out of Titanium." Would that work? Like would it hold? Would it float?
Anytime you scale something you have to make compromises because physics does not scale linearly in many ways. You have to decide what your goal is, and make decisions accordingly.
Its pretty clear you are not going to make a weapon, because a scaled battle ship would be a pretty poor one. So there is no reason to attempt to make the thing "bullet proof". Besides there is no such thing as bullet proof because there is always a bigger gun. I corrected your title because "titanium" and "on a budget" don't go together.
If you are genuinely interested in building a scale model that floats I would first recommend fabricating a small boat from a plan or kits. This will allow you to learn the fabrication process before getting weighed down with the details of your specific project. You have to eat the elephant one bite at a time and that means starting with and completing small projects and working up to big ones.
I question if you have really thought through what you're asking here.
A 1/50 scale Yamato "boat" would be 5.25 meters long. It almost doesn't matter what you build it out of, the materials required to support a 5m boat are orders of magnitude less than a 265m one. You can build it out of whatever you like, there are tons of aluminum or steel boats out there to start with. Trying to engineer a 15 foot boat would take more effort than just going and doing it. I would just find others who have already done this (you aren't the first) and share information.
None of the drawing dimensions would scale, mostly because you don't have to support the immense weight of the full-size design. You also aren't going to power it with 15 1/50 scale boilers, main and electrical turbines, 4 screws, etc. since the cost of this would be more than the structure. Nor could you join the materials with 1/50 scale welds. Creating a scale version of main gun turrets would be cost prohibitive as well, unless you're just taking some 9mm rifle barrels and sticking them in a rotating mechanism. In the US, this type of thing will need to fall within the National firearms Act, you can't just build firearms however you want.