Both my airheads were greatly improved when I fitted a pair of the new Michelin pilot series tyres that are properly sized to be 3.25 and 4.00. Handling was much quicker AND more stable that the original BT45s. This is a good combination, in the wet or dry.
I found that my nominal 4.00 BT45 was in actually 118mm in width, so nearly a 120.
On your bike a 120 should fit with a bit of grunt in fitting it, if it rubs on the swinging arm there used to be a spacer that could be fitted to the hub to move the wheel away from the swinging arm.