As discussed in the posts above its going to depend on the individual ship as well as the camouflage scheme worn. For a Western Approaches scheme white inside the shield and on the gun is quite likely, with working parts such as the breech in bare steel.
Depth charges usually arrived painted in a grey colour. For the RN this was usually something approximating Home Fleet Grey, for the USN it was 5D Dark Gray until this the stocks of this ran out, then Ocean Gray for the rest of the war. Some ships took camouflage to extremes and painted depth charges to match the background camouflage scheme, but this was likely rare in ships regularly using their depth charges - why repaint something you are going to chuck over the side shortly? Even when painted to match the camouflage care would be taken to avoid gumming up the primer and fuze setters on the end caps, so the end caps are frequently left in the base grey colour anyway.
It really does vary from ship to ship, escort group to escort group, and within each from time to time. When painting my Frigate, HMS Conn in a 1945 Admiralty ‘C’ Scheme, I painted the guns and weather shield interiors to match the overall white camouflage, with a bit of dulling down and wear, and left the depth charges in Home Fleet Grey - they used a lot of depth charges and the darker paint matched the photographic evidence. Go to the IWM site and search for photos of corvettes and you will find lots of examples.
Cheers
Steve