The addition of new words in handwritten documents such as bank cheques, bills, and notes is considered as common crime. Such immoral activities on handwritten documents have a bad effect on the victim in terms of mental and financial loss. For facilitating an impartial judicial process, it is important to differentiate between the used pen inks. Earlier, image processing and pattern recognition-based techniques for pen ink differentiation gained attention among researchers due to their non-destructive nature. Existing techniques use various colour models to represent the colour of pen inks. Thus, it is crucial to assess the capabilities of various colour models for differentiating pen inks in handwritten documents. In this paper, we propose a histogram distance based quantitative assessment technique for suitable colour model identification for differentiating pen inks. Seven blue and seven black pen ink samples are acquired on 112 cheque leaves. The k-means binarisation is used to identify pen ink pixels. $YC_{\rm b}C_{\rm r}$YCbCr colour model has been identified as the best colour model for this task. The statistical features of the ink colours in the identified colour model representation are extracted and a multi-layer perceptron (MLP) classifier validates the capability of the identified colour model for pen ink discrimination.