Why what - what won't it be cheap?
Because the big lie about jewellers is the massive mark-up they make between the cost of raw gold/platinum and diamonds and the price of the finished product - lets call it around 100%. OK, so part of that is the design/manufacturing cost.
So the way I'd do this is to sell the rings as second-hand (if you must on financial ground - otherwise keep - you might later regret it) and respecify a new one. Melted down rings have little base metal / gemstone value compared to their original price.