I don't think there was any need for plausible deniability and there was no blowback from state authorities, who were probably happy to have the Confederates cleared out. In point of fact, when the raid was over the press played up the big party held in Ste. Genevieve Mo. celebrating its success. The women of Prairie du Rocher came over with picnic baskets and fed the troops and presented a flag to Milks and a big dance was then held. Not the usual aftermath of a scandalous invasion.
Milks was arrested and court-martialed in the raid's aftermath, but not for making the raid or for attacking a band of Confederates while acting in the immediate defense of the state, which was his job. He was arrested for what happened once he was in Illinois--allegations were made that he was a little too rough once he was there. He was tried and promptly acquitted, after which the two men complaining about Milks were arrested, tried for making false charges, were convicted, and were fined $250 and $400.
This raid was not that big of a deal and was quickly forgotten.