While you can substitute weighted hiking for running, none of our plans recommend weighted hiking in the first few weeks. We normally reserve that until after the transition and base periods. Running is a more useful modality for many because they don’t have access to steep terrain. Trail running is the preferred training method of most of the top alpinists I’ve worked with. It transfers over very well to alpine climbing. However if a high volume of running might lead to an injury for you then a mix of running and hiking will be best.
The only time I would recommend weighted hikes in the early stages of a training plan is if the athlete did not have ADS. If you have ADS then ditch the pack and just work on improving your aerobic base before adding weight.