He could try to do this, but barring exceptional circumstances, the classification wouldn't hold up if the person had to actually use the pardon. And the fact that he tried to conceal the pardon would likely cause an even larger political backlash than if he had just pardoned openly.
The President can classify information. But, although he has some discretion, he cannot just classify anything he wants and expect it to be legally enforceable.
18 USC § 793, which covers disclosing classified information, pretty much requires that information be "respecting the national defense" if you want to prosecute someone for disclosing it. Also, if you start classifying information for no good reason, that goes afoul of the First Amendment freedoms of speech and press. So, how exactly does the secrecy of this pardon positively impact the national defense? The courts may ordinarily give some deference to a President's say-so, but not if it's a clear-cut abuse of the power.
I suppose it's possible that the pardon is related to illegal actions during secret ops that are legitimately defense-related. Revealing the existence of the pardon would then be tantamount to admitting the existence of those secret ops, so the pardon could justifiably be kept secret. But this scenario seems rather unlikely to be applied to a presidential candidate. And if a bunch of prosecutors already know about it and think they can convince a jury beyond a reasonable doubt, it seems likely that the cat is already out of the bag regarding the ops, and there's little justification to continue to keep the pardon secret.