Ok, what I need is the diameter across the base of the projectile (above the brass cartridge case)? I think I know what it is, but it will take some digging to confirm and I need that measurement to bemore sure. Preferably in milimeters if you have calipers or something.

The top portion looks to be a mechanical time fuze. The two grooves are to screw it on with a fuze wrench. Those numbers are an indication of a some delay, which is set to ensure an air burst, rather than a point detonating fuze which detonates the shell on impact. I should be able to confirm more details once I know the projectile type.

Do you have any more details about when and where this item came into private posession? And not to insult your intelligence, but how sure are you that it is an inert round? At least in the US, our WWII generation was notorious for bringing live ammunition home, to the shock of small town law enforcement officials when they are finally discovered. Keep in mind that Target Practice rounds may have live propellant and tracers.

My heart rate spiked as a modern Explosive Ordnance Clearance Agent, because in modern NATO practice, inert projectile for training are painted sky blue, not black.

The caliber of the shell makes me think it is from a artillery piece, but i do not know of any 4.25" artillery pieces. The british used a 4.5" howitzer and the germans used 10.5 cm howitzers (roughtly 4.13") as did the americans. The americans used a 4.2" mortar but it seems unlikely. It is also possible that it is from a naval gun, but i am not sure. Where did you find/get the shell? Could you try to get the precise calibre of the shell? If it is 4.5" it seems possible that it is from a 4.5" gun as thr weight matches.

Which country is this in? And do you have any photos of the base of the casing? Markings there are used to distinguish types of shell.