From Navweps Bofors 40 mm/60 (1.57") Model 1936 used a [FONT=Arial,Helvetica]1.960 lbs. (0.889 kg) AP M81A1 shell (so no to 5lb) that goes through [/FONT][FONT=Arial,Helvetica]1.20" (30 mm)[/FONT] at [FONT=Arial,Helvetica]2,000 yards (1,829 m)(and at 0 yards you get [/FONT][FONT=Arial,Helvetica][FONT=Arial,Helvetica]2.70" (69 mm)) but you do get 2 per second (if you can keep it feed) [/FONT][/FONT]
Apart from the fact that the ships are to the west of the UK and you have to fly from the east (so only a few very large Condors can really do it) and the merchant ships are not unarmed they have gun on them .5/20mm/3'/4' all later than on warships but still you are a fragile target compared to a ship and a long way from home are you really going to walk .5 fire onto a ship with its own .5s (and bigger stuff)... (I'm also not sure that 30x40mm hits will sink most merchant ships (unless you hit the right parts most of yours will hit the top and grouped together from each burst)
-But any big aircraft will be expensive (range and load are not cheap)
-But the German navy isn't allowed that many aircraft (aircraft are for the Luftwaffe)
-But the Luftwaffe is concentration on supporting the German army ( and without that you don't get bases in France/Norway and you need much bigger aircraft)
- The British have a lot of ships (just to make it harder for you)
- if you get down to 1000 yards (to hit accurately) then the ships will get some hits (and aircraft can take a lot less than ships).
- Turrets make you deal with deflection shooting, nobody was good at deflection shooting unless they are very good (1% of pilots) or they had late war giro gun sights (1944+)
- OTL turrets guns don't have a good history, they are much heaver than fixed weapons and spoil the aircraft's speed and they miss a lot need more crew and cost much more .....
- Just hitting ships was hard (from a range and speed that was survivable v defensive fire) hitting just under the waterline will be very hard (and to far under the water and shells will slow down to much) I think most hits will be in well above the water line.
Personally I would go with high velocity folding fin rockets (R4M) from fighterbombers but you cant as they are 1944+