Could the difference between absorption time of Diclofenac Sodium and Diclofenac Potassium be related to the cation?
Under physiological conditions, the counter-ion is almost entirely dissociated from the drug, meaning that the identity of the counter-ion isn't directly responsible for how well a drug performs. This has been looked at extensively by medicinal/formulation chemists, who often screen many salt forms looking for desirable properties. 

From the graph below, you can see that the plasma concentration curves are essentially identical for sodium, potassium, and calcium salts (slight variation in Cmax and Tmax but within experimental error): 



Source: Drug Like Properties: concepts, structure, design and methods, Chapter 7

One case in which the identify of the cation does matter is where there is a common ion in the body. This 'common ion' effect is most common when amine drugs are presented as their hydrochloride salts. The stomach is acidic (hydrochloric acid), and therefore the presence of a high concentration of chloride ions can prevent the salt from turning into the free drug. 

What is likely to be different between different cations the form that the salt takes. Different salt forms have different packings (some might be amorphous, some might be highly crystalline and ordered). The formulation may also differ (powder coated tables vs gelatine capsules), which will change the time it takes for the drug to be released/absorbed.