I would recommend you bring your own, along with a power strip. There is a hand-held dryer in Concierge Class (in addition to the wall mounted one in the bathroom) but that is not very powerful. The power strip will come in handy for recharging cell phone, camera batteries, etc. There is only one outlet, by the desk. The one in the bathroom is for razors only. Or you can always sit out on your balcony and let the wind dry your hair!
Have fun in Alaska!