In Avengers: Infinity War, it's shown that the MCU Peter's web-shooters can, like Iron Man's armor, self-assemble when activated. Strangely, not every version of Spider-Man uses web-shooters.

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[Joel Creates] is one such example with his Spider-Man wrist-mounted web-shooters. Previously, [Joel] had built a web-slinging system based around a pressurized tank of hot glue worn like a backpack.