My first idea is to make the knowledge checks (and field of study) myself and to keep the results hidden, thereby keeping a newly discovered monster's creature-type (and by extension its templated abilities & immunities) a 'state secret', as well as concealing its assigned rarity in the world. Perhaps the PCs will be able to recognize the monster by its general appearance and movement based on legends they've heard, but again the exact monster type won't be automatically known to them, nor any but its most common traits.
Making the checks secretly seems like the proper solution. Alternatively, you could just make them passive checks (assume the PCs always Take 10 on these Knowledge checks and you can simply compare the party's highest scores to the Knowledge DC of the monster).
OTOH, you shouldn't be making the checks secretly just so you don't have to give info to the players: There are lots of creatures and monsters that it would be logical for the PCs to recognize.
On the gripping hand, I think the rules for identifying creatures with monster checks are positively ridiculous. A higher CR shouldn't make it more difficult to recognize a monster. Quite the contrary: The more dangerous a creature is, the more likely for it to be famous far-and-wide. Smaug should not be difficult for the local villagers to recognize.
Creature knowledge should be based on the rarity of that information and
nothing else. Information can range from the obvious ("that's a humanoid; it's got two arms, two legs, and a head") to the general ("that's a troll-spawn, one of many creatures magically created from troll-stock") to the specific ("that's a blue-speckled troll-spawn; don't hit it with metallic weapons or you'll get hit with a nasty electrical shock") to the esoteric ("blue-speckled troll spawn were created by the Archmage Findallius in the 3rd century RD").
In general, I just set a DC identifying the creature by name. Score a little below that and you might be able to draw some broad conclusions about its characteristics from general observation. And for every point or two you score above the DC, I'll start handing out specific mechanical information about its abilities.