I would bet that they sent the Conscience / Lenore / Riley to Wah first as a sort of pathfinder, because it was the least desirable of the four heroes with its short emitter, just in case they did not like the modifications he did; they would still have 3 of the best heroes on hand. After they got the modified phaser back, kind of a proof of what they would look like, then they sent the other 3. It's all speculation of course but it seems a logical progression. You would not want to risk all of your $7000* dollar props!
* Herb Solo mentioned this figure in a letter to Ernie Scanlon from 9-28-66 where he writes " . . . have you ever heard how much our phaser pistols cost us for STAR TREK? Would you believe a minimum of $7000.00? And would you believe that they were not insertable after completion?"
Makes sense.