Of course, you can add withTaskCancellationHandler inside withTimeout.
But probably you can leave it to the operation to decide how the cancellation needs to be handled.
You can pass your non-supporting operation wrapped with withTaskCancellationHandler and then pass to withTimeout.
Also, handling cancellations with an actor is probably not what you should do.
Look at the thread How to use withTaskCancellationHandler properly? which extensively tries to exhaust this topic.