I'd have to see the exact wording on Blood Shield, but I don't see why you can't attempt a cleanse with 0 skill.
1) The rules say a hero can attempt to cleanse an area as an action.
2) There is no further exceptions mentioned regarding characters with 0 skill.
3) Even with 0 skill it's possible to gain dice through teamwork.
4) It's possible to skip your action anyway, so it's not like this could ever be some weird corner case method of cheesing the rules.
5) For comparison, if you somehow get 0 attack, it has to be possible for the Sin to start a fight with you in order for the game to work,and if you can participate in a fight, there's no reason you can't start one.
I've played you can clease with zero skill. You can also gain dice by taking a corruption to boost the roll, should those bonuses be available.