I'm guessing that the challenges with Ti would be the similar to welding aluminum - they both oxidize pretty much immediately when exposed to air, so I would expect you would need shielding gasses when welding it. TiG I expect would be the most common method, but it's not a material I had to deal with in my engineering days, so correct me if I'm wrong there...
Most case restoration is done via laser welding, and I had a look at some laser welding machines - they do sell annealed (dead soft) Ti wire for these machines, and as expected recommend that welding be done with argon shielding gas. How easy or effective this would be for case repair is a question I can't answer.
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