Why is the cop deliberately involved with the final part of the sting?

There were two reasons that the cop (Snyder) was suckered into the con:

1. As a "loose cannon," he could have blown the con by exposing Hooker or otherwise throwing a monkeywrench into the works. By making him believe that the "Feds" were in control, and by having the (fake) "Feds" intimidate Snyder into co-operating, the con-men were able to neutralize him as a threat to their con.
2. As long as they already had Snyder under control, they might as well also use him for the "blow-off." By having Lonnegan get escorted out of the premises by Snyder (whom he knows to be a legitimate member of the police), the con-men boost the verisimilitude of their con. Presumably, Snyder takes Lonnegan to a secluded place, convinces him that the "Feds" were in control, and also makes it clear to him that his (Snyder's) "best bet" would be to swallow the loss, lay low for a time, and refrain from asking too many questions (using those "feelers" that you refer to) - unless he wants to face hard time in a federal penitentary. ALSO: Remember that, early in the film, Lonnegan explains to one of his henchmen that even the mere appearance of weakness would ruin his reputation among other gangsters and spell his doom.