Single Combat vs Shroud
Yes, you can choose a shrouded permanent. And if a shrouded permanent isn't chosen, it must be sacrificed.




  702.18a Shroud is a static ability. “Shroud” means “This permanent or player can’t be the target of spells or abilities.”


When a rule or ability uses a word with a rule meaning, it only refers to that specific meaning. Target is such a word.

Only the following target:


Spells and abilities on the stack that use the word "target".
Aura spells (since the rule text for these uses the word "target").


Keep in mind that certain keyword abilities represent abilities that use the word target (e.g. Equip).

Single Combat doesn't target, so it's unaffected by Shroud.