Quick answer to your specific question...I join with what others are saying...the 30-06 will do it. I'm glad you have no concerns of your buddy's rifle shooting skills...that would be a bit of a stretch for me in your shoes, but you know him. You hand-load (as do I), so I'm sure you'll have that rifle/load dialed-in and a drop table with you. Some dry-fire should give him a feel for the trigger.
I'm sure you've thought of this option, but I'll mention it...bring both your rifles, leave the 44mag lever action at home. Have your buddy carry the '06, and you carry the 340WBY. Sh-t does happen sometimes despite our best efforts, and I would want to be able to put a finishing shot on that bull if needed...and that 340WBY will reach way out there, which might be needed before a wounded bull jumps in a lake, goes over the ridge, disappears in the thick brush, etc., etc.
Best of luck on your hunt, and an advanced welcome to Alaska!
Edit: Readers should check the regulations in advance and make some calls to ADFG and Fish/Game enforcement (Troopers) to see under what circumstantial situations, if any, the above is acceptable to do.