I think it would be a good idea to wear a helmet in a Chipmunk. I also started my flying in Chipmunks at Swinderby, but also flew them later on. Helmets and nomex suits were not just to acclimatise fast-jet students - they were mandated for passengers and cadets too.
One of the benefits of a helmet is protection from contact with the cockpit and/or canopy, which in the chipmunk is all very close.
The problem is getting one to fit, and to be compatible with your comms system. The Mk3/4 had web cradles - you still need the basic sizing correct but fine fitting is by adjustment of straps in side the shell. The Alpha/Mk10 has solid pads so you need to get hold of the correct sized pads to make it fit well.
Or you could go completely retro:
For Sale: 1960s RAF Bone Dome Helmet with inners and mask. ? FighterControl ? Home to the Military Aviation Enthusiast