Judge if your other co-founder brings value in terms of the business network with potential markets, partners or investors. If you feel that he is needed for the business to function then you should probably be looking to outsource the website. Since you have paying customers for your project, you can do a simple A/B test by announcing that you are going to release the feature in question and provide a sign up/ i am interested form. You can tell be the number of customers who would be interested in the feature versus your existing customer base.

If you genuinely feel that the non-tech co-founder is not bringing enough value to the table, you must probably be looking at buying out part or whole of the stake. However, I suggest that you get knowledge of the other aspects of the business such as accounting, tax filing norms and such. Most of the other stuff, you can find others to handle for you without parting with your equity.