Kaidan isn't on the vanilla marriage system, so you will need to get him in that faction by using Nethers Follower framework version 2.7.9, as newer versions do not allow this to be done with Kaidan. Please Note: It is not required to add him to the NFF framework. This must be done just before marrying Kaidan the usual way to work. Once you have done the steps below, Kaidan will have the unvoiced elope option in his dialogue box.

Screenshots below: