Best way to dissolve and consume cysteine HCl monohydrate powder
I wouldn't worry at all about the oxidative dimerization of cysteine to cystine when you consume freshly prepared solutions. 

In the lab, you'd use oxidants, such as $\ce{FeCl3}$ (in the presence of air) or hydrogen peroxide to achieve this reaction; both of which you're not likely to add to your amino acid diet!

As far as the article which you mentioned is concerned: The stabilization methods in question will only be relevant to maintain the composition of prefabricated and sterile-packed solutions over a long period of time.