As far as I can tell in canon, the Three were created without Sauron's influence more because of an accident of timing rather than any conscious decision on Celebrimbor's behalf.
We definitely know that the Three were the last to be made:
Now these were the Three that had last been made, and they possessed
the greatest powers. Narya, Nenya, and Vilya, they were named, the
Rings of Fire, and of Water, and of Air, set with ruby and adamant and
sapphire. (Of Rings of Power, Silmarillion)
We also know that Sauron parted company from Celembrimbor and the Elven smiths, during which time he forged the One Ring:
Sauron himself departed from Eregion about the year 1500, after the
Mírdain had begun the making of the Rings of Power. Now Celebrimbor
was not corrupted in heart or faith, but had accepted Sauron as what
he posed to be; and when at length he discovered the existence of the
One Ring he revolted against Sauron, and went to Lórinand to take
counsel once more with Galadriel. They should have destroyed all the
Rings of Power at this time, "but they failed to find the strength."
Galadriel counselled him that the Three Rings of the Elves should be
hidden, never used, and dispersed, far from Eregion where Sauron
believed them to be. (Concerning Galadriel and Celembrimbor,
Given these two facts, I think we can deduce that Celembrimbor crafted the Three after Sauron had left, in conjunction with Sauron's crafting of the One Ring. As a result Sauron had no influence on their crafting. Prior to Sauron's use of the One (although possibly after the crafting), Celembrimbor discovered the truth and helped disperse the Three amongst the Elves.