Indeed, the eucalyptus/menthol in the Green is pronounced. For me, it's brisk and refreshing. However, compared to the other Proraso creams, it has the least added parfum/fragrance (listed last in the LOI).Classic it may be, but Proraso green is certainly not the Proraso with the least scent that the OP had asked for.
Proraso is not known for subtleness, but for me the least pronounced scent is the blue, followed closely by the white, and then the red Proraso.
In addition, eucalyptus/menthol vapors don't tend to linger long after the shave (vs added parfum/fragrance), IME.