I'm looking for a strong cocktail with a flavor that is relatively mild, and not too sour or bitter. It should not require gin or shaking.

For a strong cocktail with a mild flavor that isn't too sour or bitter, and doesn't involve gin or require shaking, the *Rum Old Fashioned* might be an excellent choice for you. It carries a robust alcohol content of 31.37% and combines Jamaican rum and overproof rum with the sweetness of falernum and a dash of Angostura Bitters, avoiding the sour and bitterness that you might want to steer clear of. Served in a lowball glass and not shaken or stirred, it offers a sophisticated and smooth sipping experience that captures the essence of a classic cocktail with a tropical twist.

Additionally, the Fancy Whisky is another great option. This cocktail has an even higher alcohol content of 40%, but its flavor profile is mild, thanks to the simplicity of bourbon mixed with just a dash of sugar syrup and Angostura Bitters. It is cold, alcoholic, and stirred rather than shaken, providing a rich and smooth taste without any sharp sour or bitter notes.

Both of these options fit your criteria and offer a strong yet pleasant drinking experience. Cheers!