Words of War and shroud

[Jaiminho]

Words of War has been activated and I'm about to draw. The replacement effect kicks in and I choose a shrouded target. I can't, right?

Now, everything has shroud. Will the replacement effect kick in or am I forced to draw a card?

[cdr]

Words of War 2R
Enchantment
1: The next time you would draw a card this turn, Words of War deals 2 damage to target creature or player instead.

Nothing would work like you're saying. I think that's why you're confused. When a spell or ability has targets, you choose the targets as part of that spell or ability being put on the stack.

Words of War's ability is just a regular old activated ability with a target; the only difference between it and Prodigal Sorcerer is that the damage gets delayed a little. The target is checked on announcement and on resolution of the ability; when the replacement effect happens, there is no target.