If you are craving adventure, walking into the woods brings you straight into deep wilderness. Houses in Scalloway are sparsely dispersed, and there is plenty of forest between Scalloway and the next neighborhood, so you can encounter all sorts of wildlife hiking around this area.
If you are exhausted by the constant tree cover and seeking some horizons and sunshine, a brief hike off-road will bring you to a very large golf course. While dogs aren't allowed on the course and you must be careful if players are around, walking along the perimeter of the course can be a welcome relief from the trees.
If you would rather stick to the roads, views of the forest are still lovely from the street. The gently rolling hills are conducive to rolling on a bike or skateboard while your dog runs. Be sure your dog is well behaved and you have good control over your device, as the trees push in closely on the road and you may not have time to slow down in the grass before hitting a tree if you go off the road.
If you are tired of the trees, the nearby golf course, while not natural, is a huge attractant to all kinds of wildlife, from deer to wild turkeys and other birds. The morning or evening is a good time to hike down to the golf course and see if you can spot any wildlife creeping from the tree line onto the course in search of grass or bugs.