'acknowledging wariness' is correct and can be used in written English.
It means to acknowledge or recognize someone's cautious or suspicious attitude towards something. Example: The new employee was hesitant to trust her coworkers, acknowledging her wariness after her previous negative work experience.
Even magazines like Guns & Ammo, the Vogue of firearms, had to acknowledge the initial wariness of some readers.
But the roundtable participants also acknowledged a general wariness – verging on paranoia – in the public sector about opening up too much.
On Facebook, Twitter and the comments section of the article on The Times' Web site, people expressed wariness about giving more personal information to the social network, while also acknowledging that the service could be a boon for Facebook if managed correctly.
Second, the point made above even makes more sense when acknowledging that there seems to be a logical inconsistency between behavioral inhibition as defined by wariness towards the unfamiliar and the impairment characteristic of SM which often involves familiar social partners (e.g., classmates) and situations (e.g., school, for a discussion, see [ 30, 31]).
City officials acknowledge that they must go green in a way that is consistent with Houston's wariness of regulation.
But they acknowledged that anger over American policies -- and resentment of American power -- had translated into varying degrees of wariness, discomfort and even risk for Americans living in different parts of the world.
A senior Afghan official acknowledged "divisions" in the presidential palace over the matter between those with pro-Western sympathies within President Karzai's inner circle, and those whose wariness of America and its objectives in Afghanistan runs deep.
Acknowledge, acknowledge!
Army officials acknowledged that the idea could streamline their force planning, by giving them only one mission to fulfill — although some Army officers also expressed wariness that the Marines were trying to move from an unpopular war, Iraq, to Afghanistan, which has more popular support.
A8 Wariness in Macedonia NATO said it would send 3,500 troops over the next two weeks to collect weapons from ethnic Albanian guerrillas, but it also acknowledged the deep skepticism among the majority Macedonian Slavs, who say they do not believe the rebels will give up all their arms and fear that NATO will become a permanent presence.
