WWII era APDS ammo was inaccurate to the point where a 1944 U.S. Army test concluded standard AP was overall superior. Germany must have reached a similiar conclusion as APDS ammo was not mass produced despite several development programs including APFSDS from smoothbore cannon. I prefer tank cannon able to hit the broad side of a barn so let's cross that option off the list.
The British, on the other hand, have concluded that APDS was a very useful thing, and it was the part of ammo supply for 3 gun calibers of the ww2. The 'regular' AP ammo still be carried in the tank, as it was probably practice in British army.
HE capacity is just as important as AP. U.S. Army considered their 76mm HE shell to be poor. Perhaps a better HE shell could have been designed but if that were possible then why didn't it happen historically?
The 76mm HE shell was poor because it was consisted of too much steel and too little HE filler, being tailored to withstand the stresses when it was fired in the gun chamber. US Army can order the cartridge with reduced propellant (= less stress during firing), featuring the bigger/longer HE shell, with thinner walls much greater HE filler.
Why did it not happened? Well, it took some arms twisting to get the 76mm into Sherman, and 90mm was seen as the immediate future, so they thought why bother? Also, the HE and AP shells with almost the same ballistic properties could use the same sights - not the case when one is, say, 15 lbs, another is 10 lbs.
German 7.5cm/48 cannon has a good HE shell and decent AP performance in a relatively lightweight and inexpensive package. That's why it's my first choice for a WWII era tank / AT cannon.
It is easy to like that gun.
British 77mm/50 cannon should work if Britain develops an effective HE shell for the weapon. Or else they could simply copy a captured German KwK40 cannon. Either way they need to get moving. British Sherman tanks should receive the upgrade before the end of 1943.
By the end of 1943, the British have 17pdr in production for a year or so. Even with the APCBC ammo it can kill the Tiger under 1,5 km. The 75mm HV should allow for easier installation and greater ammo count, however. The 77mm HV was a later gun, 75mm HV and 17 pdr being earlier ones.