'Law of Surprise' + episode 8

I have a question regarding the 'law of surprise' and how this episode hilariously shown destiny giving Geralt the middle finger. My question is whether or not Geralt has a say in his reward or if the reward is completely decided by destiny?

In this episode the merchant suggests Geralt invoke the 'law of surprise' as payment, which Geralt refuses. What if Geralt accepted this suggestion and invoked the 'law of surprise'. Upon the merchant arriving home it would have been obvious to the merchant and wife that Ciri is the reward that destiny has decided. Now we all know Geralt already has this claim through the very same means however the Merchant and wife do not. Would Geralt be able to deny the reward in favour of something else or would it be too obvious to the couple that destiny is pairing Geralt and Ciri?