A complicated question in that although No.2 Commando provided the main force of Commandos, demolition units were drawn from most other Commando units. The raid date - 28 March 1942 preceded issue of green berets and Combined Operations insignia.
Several units, including No.2 were wearing tam o shanter caps. They also wore distinct embroidered insignia on arm, and a distinct cap badge. They also wore a white and black chord lanyard. Note - As Marc says above - Insignia does look to have been absent operationally ...
The best site by far for images is this one:
http://gallery.commandoveterans.org/...ery/v/units/2/
https://gallery.commandoveterans.org...+copy.jpg.html - see top centre for St Nazaire POW - wearing No.2 Cdo Other Ranks badge in his headdress.
Dress varied between troops within No.2 Cdo eg - One of the troops wore kilts on the raid.
Add the complexity of demolition parties drawn from several Commando units and the variety of potential insignia (where worn) would be quite extensive.