I, too, can't believe elm is actually extinct in Denmark. Like I mentioned in another thread, I don't live too far from Denmark (globally speaking) and we've got the disease here too. Sure, trees die left and right, but there are a lot of saplings still, and far from all big trees get infected. Also, worth thinking about is that you can still make good bows from infected trees. IF they got the disease fairly recently. If you see a tree with a dead branch or two at the top, and some branches looking healthy, the tree just caught the disease and will make a bow. You may have to remove a growth ring or two, but it'll work. If the bark is peeling off, it's no good.
Hazel, ash, maple, juniper, elm, rowan – all fine. Laburnum, hawthorne (which I'm sure grows in Denmark – it grows in north Germany and Sweden), lilac, and hornbeam are probably there too. I'm guessing there are places in Denmark where yew grows too. And then the fruit trees – plum, apple, pear, cherry ... Any selje-røn nearby?
Personally, I don't see there being a great difference in what kinds of wood make a good flat bow or (English) longbow. If it works for one design, it probably works for the other. Some are of course better suited for heavy warbows, unless you feel like making a 9 foot bow, but for medium weight bows (35-55 pounds or so) of either ELB design or flat design you can get away with using a lot of different kinds of wood. Some has to be made longer or wider than others though. But it's doable. Wether it's possible to make a particular bow from a particular piece of wood is largely a judgement call and the ability to make that call is something you can only learn by doing. And doing a lot of it. But you seem to have the passion for it, so welcome to the club! :-)