I would imagine you could use ash, elm or hazel and make a bow in the same draw weight range (100 - 150) while keeping it safely historically accurate. I think they would have used whatever indigenous woods they could get their hands on.
As a sidenote (sort of, it's still relevant...ish) I was chatting to Jaro Petrina last night (undisputably one of the best self-warbow makers using ash and other white woods) and he reckons white wood bows were far more common than we think. The trouble with whitewood (especially ash) in heavy draw weights is that any moisture or humidity can affect them really badly. He recommends working with extremely clean, dry hands as even sweat can cause issues with the very heavy bows if you're using ash. Anyway, point is, his theory is that commoners including farmers, workers, basic soldiers etc would have far more likely had ash warbows to practice and train with as they would have been cheap and quickly made. They would be hung over a fireplace when not in use to keep the moisture at a minimum until they were used. These bows were probably more common on the battlefield than yew bows which would have been expensive and took slightly longer to make. Yew isn't as finicky when it comes to moisture so for long campaigns and invasions they would possibly have been used, but I can see the logic that a good, honest farmer or soldier would have used a whitewood (meane wood) bow over a yew bow for everyday use. He's actually bringing out a very heavy article about that exact thing soon.
I guess it depends what you're trying to end up with - high-end expensive looking armour and equipment that would have been issued to house guards and upper class soldiers, or the tattered, worn, beaten and repaired weapons and tools that you'd find amongst mercenaries or freelancers. I know which I would rather have as decoration, but then I really like the look of "used" weapons.
I think a good chunky ash or hazel bow (go for something like 40mmX36mm in the handle and follow the basic Mary Rose Warbow shape - parallel for 30cm each side of the center, then tapering to temporary tips at 1" wide, before shaping the final 8" during tillering to 1/2" tips so you end up with two tapers along each limb) made to look old and weathered with lots of various woodstains and dents and knocks that don't affect the back of the bow so as not to risk it breaking would look amazing amongst other hand made Norse items.
