Titanium is a pretty shitty forging material, and you'd need a shitton of titanium (a fairly hard-to-find material) to make something that big.
It's logically impossible to remove mass from the main sword while still having the main sword remain the same. It's like saying you can take two grapes off a vine and have the vine stay in its original form. You can't make something out of nothing, and if you take something out of something else, the first thing will have less mass because of that.