Fwiw, BOTH the Swedish K & the first Sterling SMGs were designed (and some were issued) in late WWII.
(Someplace I have the photo of a British Red-Cap officer, who has a Sterling slung over his shoulder during Market-Garden.)
Some of the UK's paratroops had Sterling MK1 SMG then too.
(The Sterling was designed in 1943 & manufactured/fielded on "a limited basis" in 1944.)
Yes they were WW II (very late WW II) designs, but they were basically Cold War / Post-WWII weapons.
Market Garden, specifically the battle of Arnhem, saw use of STEN Mk V's and a small number of the predecessor to the Sterling, the Patchett Mk 2 SMG. For some reason I recall the number being 50 Patchett's, but don't quote me on that. The Patchett was an experimental SMG at that time. The Sterling Mk IV as you and I know it wasn't adopted until 1953.
The Patchett used at Market Garden is nearly identical to the Sterling that was eventually adopted. The gap between WW II and when it was adopted wasn't for additional development time, it was because there were so many STEN's (which were completely adequate SMG's) in the inventory so there was a lot of resistance to replace the STEN for financial reasons.
The only differences between the one adopted in 1953 and the one used at Arnhem are (from memory, so sorry if I don't list everything).
Finish - Patchett was Parkerized (as was early Sterlings), but eventually the Sterling went to the baked on wrinkle enamel it's so famous for (always loved that finish).
Muzzle cap - Sterling used a muzzle cap that aided in the use of a knife style bayonet (I think the one for Enfield "Jungle Carbine")
Magazine housing / Mag release - The magazine housing was slightly elongated and the magazine release button was greatly increased in size.
Magazine - I'm not sure if the curved magazine was used at Market garden or not (I think some were IIRC), but the magazine did get further development into what was probably the best SMG magazine ever built.
Other than those small changes, the Sterling was very much the same gun as the Patchett.
But understand the Patchett was used in VERY small numbers during WWII so I (and many others) have always thought of it really as a Cold War era weapon.
Same with the Swedish K. Designed at Karl Gustav in 1944 and adopted (in very small numbers) in 1945, it really didn't get into widespread use until the early 1950's. Actually I'm pretty sure the Egyptians made more "Port Said" M-45's than Karl Gustav ever did. But the Swedish K became a Cold War staple and most anywhere there was conflict during the Cold War, you'd find a Port Said Swedish K.
And if we're being honest, 99% of all SMG's can trace their design lineage to WW II or just before.