I am not sure it is possible to fulfil all of your requirements, but I gave it a go.
Displacement: 3,700 tons standard, 5,350 full load. (Lots of displacement devoted to fuel)
Dimensions: 410 x 44 x 18 feet
centre shaft - MAN 8-cyl. Diesel, 5,000bhp
outer shafts - geared turbines, 55,000shp
Speed: 17-18 knots diesels only, 34-37 knots with both at full output. (Highest speed would depend on lowest displacement possible)
Endurance: up to 15,000 nmi at 12 knots with mix of diesel and turbines running.
Armour: nil (1.5" box round magazines)
4 x 5.9" (2x2)
2 x 37mm (1x2)
4 x 20mm (4x1)
Torpedoes: 4 x 21" (2x2)