The 25-06 is good for medium sized game but in my opinion (based on taking 25 elk myself and seeing more than 100 others taken) it is a little on the light side for elk. Not saying it won't work. I've even seen 2 elk shot with the 25-06 and they both ended up on the game pole. But those were taken by guys that lived in elk country and they waited for a perfect broadside shot and were able to pass on questionable shots since they had the whole season to hunt. Additionally both the elk I saw shot with the 25-06 were cows and not mature bulls. Anyone that has hunted elk will tell you there is a world of difference between the 2.
All that being said, the 25-06 is a legal elk caliber (at least in my native CO) and it will work. But there are better choices (like the 7mm Mag you say you have). if you want to use the 25-06 use a premium bullet and pick you shots with the understanding you may need to pass on some shots. I wouldn't try to bust the front shoulder with it not would I try to bunch the bullet through the paunch from a quartering away shot. But on a broadside shot through the ribs it will kill any elk alive.