Isn't the purpose of the wrist twist to lock the wrist up and take out the slack so you can use it to connect to the core (via the elbow then shoulder, etc), more or less? In which case uke making their wrist stiff does part of your work for you and you can just skip that step...?? Why would it make it harder?
Not sure if you're asking me, but here's my opinion just in case: That is more true of Nikka jo/Nikyo, but regardless, don't skip any steps. I believe Kote Gaeshi is translated as more of a "forearm return" than a wrist twist, if a concept is helpful to you.
No matter what he does, commit to the completion of the technique
. If uke tenses his arm and wrist, that usually means he is going to sit down and roll, instead of taking the full breakfall. IMO, that's a good way to practice it because it's probably going to turn out that way more often (with non-ukes).