Perhaps too occupied with recovering from the initial shock of the slime's movements, Vincent hadn't noticed the concealed slime hitch a ride on his hand right away. Rather, he noticed a few seconds after he prepared his sai, noticing a trail of slime leading up from his hand onto his forearm.

At first, he froze, shocked at how he'd picked up a dangerous cling-on without realizing- but he quickly bit down on his tongue and began to think. 

The trail of slime was too long and distinct to be just from handling the vial, so the resemblance to the trail left by the slimes wasn't a coincidence; there was definitely a slime travelling up his body, he just couldn't see it.
However, it seemed that the slime hadn't made it very far- the core wasn't in the slime on his hand or forearm- and whilst he couldn't see it at the moment, he couldn't feel it on an exposed part of his body or forcing its way through his clothes. 

He had an idea, and it might just work if he was quick enough.

Without a single further word, he shucked his already-unbuttoned coat, letting it drop to the ground before he flicked his gloved hand to remove the bulk of the remaining slime. 
And then he brought his foot down hard on the outline of the slime visible beneath the fabric of the coat beneath him.