One of the best ways for calculating of DP in cellulose fibers is using of viscometric method by cellulose solvents like cupriethylenediamine (CED) and involving them in Mark-Houwink equation [η] = KM^a,
Unfortunately, I am not familiar with this technique, but I already suggest you to use viscometric technique coz it is an inexpensive and very easy way.
First you will have to determine the molecular weight of this polymer then viscometry seems to be cheaper and more available than others using appropriate solvent systems.
Otherwise, I know that for other polymers (pectin) there would be a spectrophotometric approach to determine DP. It is by determining the Total sugar content and Reducing sugars content of the same sample. Then to calculate the ratio (in molar base) among obtained values. However, you will have to check it out that you are determining accurately both values because in total sugar content the technique use a polymer hydrolysis with sulfuric acid (which could be incomplete).