Swain's writer here. The arm itself is made of pure demonic magic, the same thing he shoots with his Q. It's held together by Swain's force of will and concentration. If you look closely, you'll see there's some opacity to it; it's not solid or grown.
The demonic magic, as a whole, holds Swain together, and helps him overcome the grievous wounds he suffered in Ionia. He has a leg brace and still carries a cane (i.e., has one on hand, just in case), because even a bad ass like Swain knows he can't concentrate 100% of the time. He is the type of man to prepare for contingencies.
The demon is a demon of secrets. It's why Swain hears whispers when he collects souls, and why he's haunted by visions of a dark future. Saying anything more is kind of against demon of secrets policy. [slayer-jinx-wink]
(Sleight edit for clarity above.)