Dominance: Kneel 1 influence to choose 2 unique characters in 2 different discard piles, and put them into play, under their owners' control

Can I play this without checking that there are 2 unique characters in 2 different discard piles?

What happens if I am the only player with an unique character in my discard pile?

Then you can't play it. Targets are chosen during the initiation of an effect, and if not all targets can be chosen, the effect cannot be triggered.

The unique characters in the discard piles are targets. We know that because of the word "choose." You cannot trigger an effect unless all required targets are available. So this event cannot be played unless there are unique characters in at least 2 discard piles because you will otherwise not meet the target requirements.