You have a couple of options and since this is a walkout basement narrowing the stairs should not be a big concern. The minimum width opening through the floor assembly is 36 inches, However the stair treads above and below the opening can be less as described below. What is the goal? Increase usable floor space in the basement if so a spiral would require the least amount of floor space.R311.7.1 Width.
Stairways shall not be less than 36 inches (914 mm) in clear width at all points above the permitted handrail height and below the required headroom height. Handrails shall not project more than 4.5 inches (114 mm) on either side of the stairway and the minimum clear width of the stairway at and below the handrail height, including treads and landings, shall not be less than 31 1/2 inches (787 mm) where a handrail is installed on one side and 27 inches (698 mm) where handrails are provided on both sides.
Exception: The width of spiral stairways shall be in accordance with Section R311.7.9.1.
R311.7.10.1 Spiral stairways.
Spiral stairways are permitted, provided the minimum clear width at and below the handrail shall be 26 inches (660 mm) with each tread having a 7 1/2-inch (190 mm) minimum tread depth at 12 inches (914 mm) from the narrower edge. All treads shall be identical, and the rise shall be no more than 91/2 inches (241 mm). A minimum headroom of 6 feet 6 inches (1982 mm) shall be provided.